{"id":2265,"date":"2026-09-26T20:54:15","date_gmt":"2026-09-26T13:54:15","guid":{"rendered":"https:\/\/people.usd.ac.id\/~ydkristanto\/?page_id=2265"},"modified":"2026-09-27T18:43:15","modified_gmt":"2026-09-27T11:43:15","slug":"exploring-vertical-spring-mass-systems","status":"publish","type":"page","link":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/learning-resources\/exploring-vertical-spring-mass-systems\/","title":{"rendered":"Exploring Vertical Spring-Mass Systems"},"content":{"rendered":"\n<div class=\"wp-block-buttons is-content-justification-right\">\n<div class=\"wp-block-button is-style-outline\"><a class=\"wp-block-button__link\" href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/media-pengajaran\/eksplorasi-sistem-pegas-massa-vertikal\/\">ID<\/a><\/div>\n<\/div>\n\n\n\n<p class=\"has-drop-cap\">A spring can move back and forth when a mass is attached to it and pulled away from its resting position. But what determines how the mass moves, and how does changing the conditions affect its motion? In this interactive resource, you can experiment with a spring-mass system by changing different settings and observing what happens. You can watch the motion unfold and see how it is represented over time, then capture and compare your observations from different settings. Through these explorations, you can look for patterns and develop your own ideas about how different factors influence the motion.<\/p>\n\n\n\n<div class=\"wp-block-group alignfull has-gray-background-color has-background\"><div class=\"wp-block-group__inner-container\">\n<h3 class=\"has-text-align-center\">Seeing Springs in Motion through Graphs<\/h3>\n\n\n\n<p>Adjust the spring constant, mass, damping, and initial position. Play the animation and see how the spring&#8217;s motion is represented in its displacement-time graph.<\/p>\n\n\n\n<div class=\"wp-block-columns alignwide\">\n<div class=\"wp-block-column\">\n<figure>\n<div id=\"calculator1\" class=\"aligncenter size-full\" style=\"width: 440px; height: 440px;\"><\/div>\n<figcaption>Visualization 1: The spring in motion<\/figcaption>\n<\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column\">\n<figure>\n<div id=\"calculator2\" class=\"aligncenter size-full\" style=\"width: 440px; height: 440px;\"><\/div>\n<figcaption>Visualization 2: The graph of displacement over time<\/figcaption>\n<\/figure>\n\n<script>\n  var calculator1 = Desmos.GraphingCalculator(document.getElementById('calculator1'), {\n    expressions: false,\n    settingsMenu: false,\n    trace: false\n  });\n  var calculator2 = Desmos.GraphingCalculator(document.getElementById('calculator2'), {\n    expressions: false,\n    settingsMenu: false\n  });\n\n  var state1 = {\n    \"version\": 11,\n    \"graph\": {\n        \"viewport\": {\n            \"xmin\": -10,\n            \"ymin\": -21.931309904153355,\n            \"xmax\": 10,\n            \"ymax\": 13.931309904153355\n        },\n        \"showGrid\": false,\n        \"showXAxis\": false,\n        \"showYAxis\": false,\n        \"xAxisStep\": 2,\n        \"yAxisStep\": 2,\n        \"xAxisMinorSubdivisions\": 1,\n        \"yAxisMinorSubdivisions\": 1,\n        \"xAxisNumbers\": false,\n        \"yAxisNumbers\": false,\n        \"polarNumbers\": false,\n        \"userLockedViewport\": true,\n        \"__v12ViewportLatexStash\": {\n            \"xmin\": \"-10\",\n            \"xmax\": \"10\",\n            \"ymin\": \"-21.931309904153355\",\n            \"ymax\": \"13.931309904153355\"\n        }\n    },\n    \"expressions\": {\n        \"list\": [\n            {\n                \"type\": \"folder\",\n                \"id\": \"32\",\n                \"title\": \"Time\",\n                \"collapsed\": true\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"36\",\n                \"folderId\": \"32\",\n                \"text\": \"Time (ms):\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"33\",\n                \"folderId\": \"32\",\n                \"color\": \"#000000\",\n                \"latex\": \"t_{ms}=0\",\n                \"slider\": {\n                    \"hardMin\": true,\n                    \"min\": \"0\",\n                    \"max\": \"12681\"\n                }\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"38\",\n                \"folderId\": \"32\",\n                \"text\": \"Time (s):\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"39\",\n                \"folderId\": \"32\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"t_{s}=\\\\operatorname{round}\\\\left(\\\\frac{t_{ms}}{1000},2\\\\right)\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"41\",\n                \"folderId\": \"32\",\n                \"text\": \"Action for running the time:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"34\",\n                \"folderId\": \"32\",\n                \"color\": \"#c74440\",\n                \"latex\": \"r_{un}\\\\left(x\\\\right)=t_{ms}\\\\to t_{ms}+x\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"56\",\n                \"folderId\": \"32\",\n                \"text\": \"Reset:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"57\",\n                \"folderId\": \"32\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"r_{eset}=P\\\\to0,N\\\\to0,t_{ms}\\\\to0\"\n            },\n            {\n                \"type\": \"folder\",\n                \"id\": \"2\",\n                \"title\": \"Model\",\n                \"collapsed\": true\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"4\",\n                \"folderId\": \"2\",\n                \"text\": \"Spring constant (N\/m):\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"5\",\n                \"folderId\": \"2\",\n                \"color\": \"#388c46\",\n                \"latex\": \"k=7\",\n                \"slider\": {\n                    \"hardMin\": true,\n                    \"hardMax\": true,\n                    \"min\": \"3\",\n                    \"max\": \"30\",\n                    \"step\": \"0.1\"\n                }\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"7\",\n                \"folderId\": \"2\",\n                \"text\": \"Starting position (m):\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"8\",\n                \"folderId\": \"2\",\n                \"color\": \"#000000\",\n                \"latex\": \"y_{0}=0.6\",\n                \"slider\": {\n                    \"hardMin\": true,\n                    \"hardMax\": true,\n                    \"min\": \"-1\",\n                    \"max\": \"1\"\n                }\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"10\",\n                \"folderId\": \"2\",\n                \"text\": \"Mass (kg):\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"11\",\n                \"folderId\": \"2\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"m=0.1\",\n                \"slider\": {\n                    \"hardMin\": true,\n                    \"hardMax\": true,\n                    \"min\": \"0.01\",\n                    \"max\": \"0.25\",\n                    \"step\": \"0.01\"\n                }\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"13\",\n                \"folderId\": \"2\",\n                \"text\": \"Damping (N per m\/s):\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"14\",\n                \"folderId\": \"2\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"c=0.1\",\n                \"slider\": {\n                    \"hardMin\": true,\n                    \"hardMax\": true,\n                    \"min\": \"0\",\n                    \"max\": \"1\",\n                    \"step\": \"0.1\"\n                }\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"16\",\n                \"folderId\": \"2\",\n                \"text\": \"Calculated parameter:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"17\",\n                \"folderId\": \"2\",\n                \"color\": \"#c74440\",\n                \"latex\": \"w_{d}=\\\\sqrt{\\\\frac{k}{m}-\\\\frac{c^{2}}{4m^{2}}}\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"19\",\n                \"folderId\": \"2\",\n                \"text\": \"The block's vertical displacement as a function of time:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"20\",\n                \"folderId\": \"2\",\n                \"color\": \"#388c46\",\n                \"latex\": \"f\\\\left(x\\\\right)=y_{0}\\\\cdot e^{-\\\\frac{c}{2m}x}\\\\left(\\\\cos\\\\left(w_{d}\\\\cdot x\\\\right)+\\\\frac{c}{2m\\\\cdot w_{d}}\\\\sin\\\\left(w_{d}\\\\cdot x\\\\right)\\\\right)\\\\left\\\\{x\\\\ge0\\\\right\\\\}\",\n                \"hidden\": true\n            },\n            {\n                \"type\": \"folder\",\n                \"id\": \"43\",\n                \"title\": \"Spring and block\",\n                \"collapsed\": true\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"73\",\n                \"folderId\": \"43\",\n                \"text\": \"Background:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"74\",\n                \"folderId\": \"43\",\n                \"color\": \"#000000\",\n                \"latex\": \"y\\\\ge0\",\n                \"lines\": false,\n                \"fillOpacity\": \".2\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"75\",\n                \"folderId\": \"43\",\n                \"color\": \"#000000\",\n                \"latex\": \"y=0\",\n                \"lineWidth\": \"3\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"22\",\n                \"folderId\": \"43\",\n                \"text\": \"Equilibrium and range:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"25\",\n                \"folderId\": \"43\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"j=\\\\frac{3}{0.6}\\\\cdot\\\\operatorname{abs}\\\\left(y_{0}\\\\right)\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"24\",\n                \"folderId\": \"43\",\n                \"color\": \"#000000\",\n                \"latex\": \"-8-j<y<-8+j\",\n                \"hidden\": true,\n                \"fillOpacity\": \".15\",\n                \"lineWidth\": \"1\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"23\",\n                \"folderId\": \"43\",\n                \"color\": \"#000000\",\n                \"latex\": \"y=-8\",\n                \"lineStyle\": \"DASHED\",\n                \"lineWidth\": \"1\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"59\",\n                \"folderId\": \"43\",\n                \"text\": \"Spring:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"62\",\n                \"folderId\": \"43\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(D_{1}\\\\cos\\\\left(\\\\pi t\\\\right),-D_{2}t-D_{3}\\\\sin\\\\left(\\\\pi t\\\\right)\\\\right)\",\n                \"parametricDomain\": {\n                    \"min\": \"\",\n                    \"max\": \"\\\\frac{41}{2}\"\n                },\n                \"domain\": {\n                    \"min\": \"0\",\n                    \"max\": \"\\\\frac{41}{2}\"\n                }\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"67\",\n                \"folderId\": \"43\",\n                \"text\": \"Spring radius:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"63\",\n                \"folderId\": \"43\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"D_{1}=1\",\n                \"hidden\": true,\n                \"slider\": {\n                    \"hardMin\": true,\n                    \"hardMax\": true,\n                    \"min\": \"0\",\n                    \"max\": \"5\"\n                }\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"69\",\n                \"folderId\": \"43\",\n                \"text\": \"Half of the wavelength:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"64\",\n                \"folderId\": \"43\",\n                \"color\": \"#388c46\",\n                \"latex\": \"D_{2}=\\\\frac{1}{82}\\\\left(-7-4g\\\\left(t_{s}\\\\right)\\\\right)\",\n                \"hidden\": true,\n                \"slider\": {\n                    \"hardMin\": true,\n                    \"hardMax\": true,\n                    \"min\": \"0\",\n                    \"max\": \"1\"\n                }\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"71\",\n                \"folderId\": \"43\",\n                \"text\": \"Width:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"65\",\n                \"folderId\": \"43\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"D_{3}=0.25\",\n                \"hidden\": true,\n                \"slider\": {\n                    \"hardMin\": true,\n                    \"hardMax\": true,\n                    \"min\": \"0\",\n                    \"max\": \"1\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"61\",\n                \"folderId\": \"43\",\n                \"color\": \"#000000\",\n                \"latex\": \"x=0\\\\left\\\\{-0.5\\\\le y\\\\le0\\\\right\\\\}\",\n                \"hidden\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"60\",\n                \"folderId\": \"43\",\n                \"color\": \"#000000\",\n                \"latex\": \"x=0\\\\left\\\\{g\\\\left(t_{s}\\\\right)+1\\\\le y\\\\le g\\\\left(t_{s}\\\\right)+1.5\\\\right\\\\}\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"45\",\n                \"folderId\": \"43\",\n                \"text\": \"Block:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"46\",\n                \"folderId\": \"43\",\n                \"color\": \"#388c46\",\n                \"latex\": \"g\\\\left(x\\\\right)=\\\\frac{3}{0.6}\\\\cdot f\\\\left(x\\\\right)-8\",\n                \"hidden\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"54\",\n                \"folderId\": \"43\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\operatorname{polygon}\\\\left(\\\\left(-1,g\\\\left(t_{s}\\\\right)-1\\\\right),\\\\left(1,g\\\\left(t_{s}\\\\right)-1\\\\right),\\\\left(1,g\\\\left(t_{s}\\\\right)+1\\\\right),\\\\left(-1,g\\\\left(t_{s}\\\\right)+1\\\\right)\\\\right)\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"136\",\n                \"folderId\": \"43\",\n                \"text\": \"Equilibrium:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"137\",\n                \"folderId\": \"43\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(-9.8,-8\\\\right)\",\n                \"showLabel\": true,\n                \"label\": \"Equilibrium\",\n                \"hidden\": true,\n                \"labelOrientation\": \"above_right\",\n                \"labelSize\": \".8\"\n            },\n            {\n                \"type\": \"folder\",\n                \"id\": \"77\",\n                \"title\": \"Controller\",\n                \"collapsed\": true\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"85\",\n                \"folderId\": \"77\",\n                \"text\": \"Spring constant (N\/m):\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"78\",\n                \"folderId\": \"77\",\n                \"color\": \"#000000\",\n                \"latex\": \"y=1.5\\\\left\\\\{-8\\\\le x\\\\le-4\\\\right\\\\}\",\n                \"colorLatex\": \"c_{white}\",\n                \"lineWidth\": \"10\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"153\",\n                \"folderId\": \"77\",\n                \"color\": \"#c74440\",\n                \"latex\": \"k_{text}=\\\\operatorname{round}\\\\left(k,1\\\\right)\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"106\",\n                \"folderId\": \"77\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(\\\\frac{4}{27}\\\\left(k-3\\\\right)-8,1.5\\\\left\\\\{t_{s}=0\\\\right\\\\}\\\\right)\",\n                \"showLabel\": true,\n                \"label\": \"${k_{text}}\",\n                \"labelOrientation\": \"below\",\n                \"labelSize\": \".6\",\n                \"pointSize\": \"6\",\n                \"movablePointSize\": \"6\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"148\",\n                \"folderId\": \"77\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(\\\\frac{4}{27}\\\\left(k-3\\\\right)-8,1.5\\\\left\\\\{t_{s}>0\\\\right\\\\}\\\\right)\",\n                \"showLabel\": true,\n                \"label\": \"${k_{text}}\",\n                \"dragMode\": \"NONE\",\n                \"labelOrientation\": \"below\",\n                \"labelSize\": \".6\",\n                \"pointSize\": \"6\",\n                \"movablePointSize\": \"6\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"90\",\n                \"folderId\": \"77\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(-8.2,1.5\\\\right)\",\n                \"showLabel\": true,\n                \"label\": \"3\",\n                \"hidden\": true,\n                \"labelOrientation\": \"left\",\n                \"labelSize\": \".6\",\n                \"pointOpacity\": \".9\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"91\",\n                \"folderId\": \"77\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(-3.8,1.5\\\\right)\",\n                \"showLabel\": true,\n                \"label\": \"30\",\n                \"hidden\": true,\n                \"labelOrientation\": \"right\",\n                \"labelSize\": \".6\",\n                \"pointOpacity\": \".9\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"92\",\n                \"folderId\": \"77\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(-6,2.25\\\\right)\",\n                \"showLabel\": true,\n                \"label\": \"Spring constant (N\/m):\",\n                \"hidden\": true,\n                \"labelSize\": \".6\",\n                \"pointOpacity\": \".9\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"87\",\n                \"folderId\": \"77\",\n                \"text\": \"Mass (kg):\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"82\",\n                \"folderId\": \"77\",\n                \"color\": \"#000000\",\n                \"latex\": \"y=1.5\\\\left\\\\{-2\\\\le x\\\\le2\\\\right\\\\}\",\n                \"colorLatex\": \"c_{white}\",\n                \"lineWidth\": \"10\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"154\",\n                \"folderId\": \"77\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"m_{text}=\\\\operatorname{round}\\\\left(m,2\\\\right)\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"113\",\n                \"folderId\": \"77\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(\\\\frac{50}{3}\\\\left(m-0.01\\\\right)-2,1.5\\\\left\\\\{t_{s}=0\\\\right\\\\}\\\\right)\",\n                \"showLabel\": true,\n                \"label\": \"${m_{text}}\",\n                \"labelOrientation\": \"below\",\n                \"labelSize\": \".6\",\n                \"pointSize\": \"6\",\n                \"movablePointSize\": \"6\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"149\",\n                \"folderId\": \"77\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(\\\\frac{50}{3}\\\\left(m-0.01\\\\right)-2,1.5\\\\left\\\\{t_{s}>0\\\\right\\\\}\\\\right)\",\n                \"showLabel\": true,\n                \"label\": \"${m_{text}}\",\n                \"dragMode\": \"NONE\",\n                \"labelOrientation\": \"below\",\n                \"labelSize\": \".6\",\n                \"pointSize\": \"6\",\n                \"movablePointSize\": \"6\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"93\",\n                \"folderId\": \"77\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(-2.2,1.4\\\\right)\",\n                \"showLabel\": true,\n                \"label\": \"0.01\",\n                \"hidden\": true,\n                \"labelOrientation\": \"below\",\n                \"labelSize\": \".6\",\n                \"pointOpacity\": \".9\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"94\",\n                \"folderId\": \"77\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(2.2,1.4\\\\right)\",\n                \"showLabel\": true,\n                \"label\": \"0.25\",\n                \"hidden\": true,\n                \"labelOrientation\": \"below\",\n                \"labelSize\": \".6\",\n                \"pointOpacity\": \".9\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"95\",\n                \"folderId\": \"77\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(0,2.25\\\\right)\",\n                \"showLabel\": true,\n                \"label\": \"Mass (kg):\",\n                \"hidden\": true,\n                \"labelSize\": \".6\",\n                \"pointOpacity\": \".9\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"89\",\n                \"folderId\": \"77\",\n                \"text\": \"Damping (N per m\/s):\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"83\",\n                \"folderId\": \"77\",\n                \"color\": \"#000000\",\n                \"latex\": \"y=1.5\\\\left\\\\{4\\\\le x\\\\le8\\\\right\\\\}\",\n                \"colorLatex\": \"c_{white}\",\n                \"lineWidth\": \"10\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"155\",\n                \"folderId\": \"77\",\n                \"color\": \"#388c46\",\n                \"latex\": \"c_{text}=\\\\operatorname{round}\\\\left(c,1\\\\right)\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"119\",\n                \"folderId\": \"77\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(4c+4,1.5\\\\left\\\\{t_{s}=0\\\\right\\\\}\\\\right)\",\n                \"showLabel\": true,\n                \"label\": \"${c_{text}}\",\n                \"labelOrientation\": \"below\",\n                \"labelSize\": \".6\",\n                \"pointSize\": \"6\",\n                \"movablePointSize\": \"6\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"150\",\n                \"folderId\": \"77\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(4c+4,1.5\\\\left\\\\{t_{s}>0\\\\right\\\\}\\\\right)\",\n                \"showLabel\": true,\n                \"label\": \"${c_{text}}\",\n                \"dragMode\": \"NONE\",\n                \"labelOrientation\": \"below\",\n                \"labelSize\": \".6\",\n                \"pointSize\": \"6\",\n                \"movablePointSize\": \"6\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"96\",\n                \"folderId\": \"77\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(3.8,1.5\\\\right)\",\n                \"showLabel\": true,\n                \"label\": \"0\",\n                \"hidden\": true,\n                \"labelOrientation\": \"left\",\n                \"labelSize\": \".6\",\n                \"pointOpacity\": \".9\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"97\",\n                \"folderId\": \"77\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(8.2,1.5\\\\right)\",\n                \"showLabel\": true,\n                \"label\": \"1\",\n                \"hidden\": true,\n                \"labelOrientation\": \"right\",\n                \"labelSize\": \".6\",\n                \"pointOpacity\": \".9\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"98\",\n                \"folderId\": \"77\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(6,2.25\\\\right)\",\n                \"showLabel\": true,\n                \"label\": \"Damping (N per m\/s):\",\n                \"hidden\": true,\n                \"labelSize\": \".6\",\n                \"pointOpacity\": \".9\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"121\",\n                \"folderId\": \"77\",\n                \"text\": \"Starting position:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"127\",\n                \"folderId\": \"77\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(0,5\\\\left(y_{0}+1\\\\right)-13\\\\left\\\\{t_{s}=0\\\\right\\\\}\\\\right)\"\n            },\n            {\n                \"type\": \"folder\",\n                \"id\": \"129\",\n                \"title\": \"Button\",\n                \"collapsed\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"138\",\n                \"folderId\": \"129\",\n                \"color\": \"#c74440\",\n                \"latex\": \"P=0\",\n                \"slider\": {\n                    \"hardMin\": true,\n                    \"hardMax\": true,\n                    \"min\": \"0\",\n                    \"max\": \"1\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"139\",\n                \"folderId\": \"129\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"N=0\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"151\",\n                \"folderId\": \"129\",\n                \"color\": \"#c74440\",\n                \"latex\": \"N_{state}=0\",\n                \"slider\": {\n                    \"hardMin\": true,\n                    \"min\": \"0\",\n                    \"step\": \"1\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"152\",\n                \"folderId\": \"129\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"M_{state}=\\\\operatorname{mod}\\\\left(N_{state},5\\\\right)+1\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"131\",\n                \"folderId\": \"129\",\n                \"text\": \"Play\/Pause:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"132\",\n                \"folderId\": \"129\",\n                \"color\": \"#388c46\",\n                \"latex\": \"\\\\operatorname{polygon}\\\\left(\\\\left(9.5,5.5\\\\right),\\\\left(5.5,5.5\\\\right),\\\\left(5.5,4\\\\right),\\\\left(9.5,4\\\\right)\\\\right)\",\n                \"lines\": false,\n                \"colorLatex\": \"c_{white}\",\n                \"fillOpacity\": \"1\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"133\",\n                \"folderId\": \"129\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\operatorname{polygon}\\\\left(\\\\left(9.5,5.5\\\\right),\\\\left(5.5,5.5\\\\right),\\\\left(5.5,4\\\\right),\\\\left(9.5,4\\\\right)\\\\right)\",\n                \"lines\": true,\n                \"fillOpacity\": \"0\",\n                \"lineWidth\": \"1.5\",\n                \"clickableInfo\": {\n                    \"enabled\": true,\n                    \"latex\": \"P\\\\to1-P,N\\\\to N+1\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"141\",\n                \"folderId\": \"129\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"\\\\operatorname{mod}\\\\left(N,2\\\\right)\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"140\",\n                \"folderId\": \"129\",\n                \"color\": \"#388c46\",\n                \"latex\": \"p_{lay}=\\\\left\\\\{\\\\operatorname{mod}\\\\left(N,2\\\\right)=0:1,0\\\\right\\\\}\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"134\",\n                \"folderId\": \"129\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(\\\\frac{9.5+5.5}{2},\\\\frac{5.5+4}{2}\\\\left\\\\{p_{lay}=1\\\\right\\\\}\\\\right)\",\n                \"showLabel\": true,\n                \"label\": \"Play\",\n                \"hidden\": true,\n                \"labelSize\": \".8\",\n                \"pointOpacity\": \".9\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"142\",\n                \"folderId\": \"129\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(\\\\frac{9.5+5.5}{2},\\\\frac{5.5+4}{2}\\\\left\\\\{p_{lay}=0\\\\right\\\\}\\\\right)\",\n                \"showLabel\": true,\n                \"label\": \"Pause\",\n                \"hidden\": true,\n                \"labelSize\": \".8\",\n                \"pointOpacity\": \".9\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"144\",\n                \"folderId\": \"129\",\n                \"text\": \"Reset:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"145\",\n                \"folderId\": \"129\",\n                \"color\": \"#c74440\",\n                \"latex\": \"\\\\operatorname{polygon}\\\\left(\\\\left(4.5,5.5\\\\right),\\\\left(0.5,5.5\\\\right),\\\\left(0.5,4\\\\right),\\\\left(4.5,4\\\\right)\\\\right)\",\n                \"lines\": false,\n                \"colorLatex\": \"c_{white}\",\n                \"fillOpacity\": \"1\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"146\",\n                \"folderId\": \"129\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\operatorname{polygon}\\\\left(\\\\left(4.5,5.5\\\\right),\\\\left(0.5,5.5\\\\right),\\\\left(0.5,4\\\\right),\\\\left(4.5,4\\\\right)\\\\right)\",\n                \"lines\": true,\n                \"fillOpacity\": \"0\",\n                \"lineWidth\": \"1.5\",\n                \"clickableInfo\": {\n                    \"enabled\": true,\n                    \"latex\": \"r_{eset},N_{state}\\\\to N_{state}+1\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"147\",\n                \"folderId\": \"129\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(\\\\frac{4.5+0.5}{2},\\\\frac{5.5+4}{2}\\\\right)\",\n                \"showLabel\": true,\n                \"label\": \"Reset\",\n                \"hidden\": true,\n                \"labelSize\": \".8\",\n                \"pointOpacity\": \".9\"\n            },\n            {\n                \"type\": \"folder\",\n                \"id\": \"80\",\n                \"title\": \"Colors\",\n                \"collapsed\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"81\",\n                \"folderId\": \"80\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"c_{white}=\\\\operatorname{rgb}\\\\left(255,255,255\\\\right)\"\n            }\n        ],\n        \"ticker\": {\n            \"handlerLatex\": \"\\\\left\\\\{P=1:r_{un}\\\\left(\\\\operatorname{dt}\\\\right),r_{un}\\\\left(0\\\\right)\\\\right\\\\}\",\n            \"playing\": true,\n            \"open\": true\n        }\n    },\n    \"includeFunctionParametersInRandomSeed\": true,\n    \"doNotMigrateMovablePointStyle\": true,\n    \"backmigrated\": 14\n};\n  var state2 = {\n    \"version\": 11,\n    \"graph\": {\n        \"viewport\": {\n            \"xmin\": -2,\n            \"ymin\": -2,\n            \"xmax\": 12,\n            \"ymax\": 2\n        },\n        \"xAxisArrowMode\": \"POSITIVE\",\n        \"yAxisArrowMode\": \"POSITIVE\",\n        \"xAxisLabel\": \"Time (s)\",\n        \"yAxisLabel\": \"Displacement (m)\",\n        \"userLockedViewport\": true,\n        \"squareAxes\": false,\n        \"__v12ViewportLatexStash\": {\n            \"xmin\": \"-2\",\n            \"xmax\": \"12\",\n            \"ymin\": \"-2\",\n            \"ymax\": \"2\"\n        }\n    },\n    \"expressions\": {\n        \"list\": [\n            {\n                \"type\": \"folder\",\n                \"id\": \"2\",\n                \"title\": \"Given\",\n                \"collapsed\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"3\",\n                \"folderId\": \"2\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"t_{s}=6.6\",\n                \"slider\": {\n                    \"hardMin\": true,\n                    \"min\": \"0\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"4\",\n                \"folderId\": \"2\",\n                \"color\": \"#388c46\",\n                \"latex\": \"k=1\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"5\",\n                \"folderId\": \"2\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"m=0.5\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"6\",\n                \"folderId\": \"2\",\n                \"color\": \"#000000\",\n                \"latex\": \"c=0.1\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"10\",\n                \"folderId\": \"2\",\n                \"color\": \"#c74440\",\n                \"latex\": \"y_{0}=1\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"54\",\n                \"folderId\": \"2\",\n                \"color\": \"#c74440\",\n                \"latex\": \"M_{state}=1\",\n                \"slider\": {\n                    \"hardMin\": true,\n                    \"hardMax\": true,\n                    \"min\": \"1\",\n                    \"max\": \"5\",\n                    \"step\": \"1\"\n                }\n            },\n            {\n                \"type\": \"folder\",\n                \"id\": \"33\",\n                \"title\": \"Saved parameters and graphs\",\n                \"collapsed\": true\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"46\",\n                \"folderId\": \"33\",\n                \"text\": \"Saved parameters:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"37\",\n                \"folderId\": \"33\",\n                \"color\": \"#c74440\",\n                \"latex\": \"K=\\\\left[\\\\right]\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"39\",\n                \"folderId\": \"33\",\n                \"color\": \"#388c46\",\n                \"latex\": \"M=\\\\left[\\\\right]\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"40\",\n                \"folderId\": \"33\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"C=\\\\left[\\\\right]\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"41\",\n                \"folderId\": \"33\",\n                \"color\": \"#000000\",\n                \"latex\": \"Y=\\\\left[\\\\right]\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"42\",\n                \"folderId\": \"33\",\n                \"color\": \"#c74440\",\n                \"latex\": \"T=\\\\left[\\\\right]\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"55\",\n                \"folderId\": \"33\",\n                \"color\": \"#c74440\",\n                \"latex\": \"L_{Mstate}=\\\\left[\\\\right]\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"43\",\n                \"folderId\": \"33\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"s_{p}=K\\\\to\\\\operatorname{join}\\\\left(K,k\\\\right),M\\\\to\\\\operatorname{join}\\\\left(M,m\\\\right),C\\\\to\\\\operatorname{join}\\\\left(C,c\\\\right),Y\\\\to\\\\operatorname{join}\\\\left(Y,y_{0}\\\\right),T\\\\to\\\\operatorname{join}\\\\left(T,t_{s}\\\\right),L_{Mstate}\\\\to\\\\operatorname{join}\\\\left(L_{Mstate},M_{state}\\\\right)\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"44\",\n                \"folderId\": \"33\",\n                \"color\": \"#388c46\",\n                \"latex\": \"c_{lear}=K\\\\to\\\\left[\\\\right],M\\\\to\\\\left[\\\\right],C\\\\to\\\\left[\\\\right],Y\\\\to\\\\left[\\\\right],T\\\\to\\\\left[\\\\right],L_{Mstate}\\\\to\\\\left[\\\\right]\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"48\",\n                \"folderId\": \"33\",\n                \"text\": \"Saved graphs:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"50\",\n                \"folderId\": \"33\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"W=\\\\sqrt{\\\\frac{K}{M}-\\\\frac{C^{2}}{4M^{2}}}\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"49\",\n                \"folderId\": \"33\",\n                \"color\": \"#c74440\",\n                \"latex\": \"f_{1}\\\\left(x\\\\right)=Y\\\\cdot e^{-\\\\frac{C}{2M}x}\\\\left(\\\\cos\\\\left(W\\\\cdot x\\\\right)+\\\\frac{C}{2M\\\\cdot W}\\\\sin\\\\left(W\\\\cdot x\\\\right)\\\\right)\\\\left\\\\{0\\\\le x\\\\le T\\\\right\\\\}\",\n                \"colorLatex\": \"c_{G}\",\n                \"lineOpacity\": \".6\",\n                \"lineWidth\": \"3\"\n            },\n            {\n                \"type\": \"folder\",\n                \"id\": \"8\",\n                \"title\": \"Model\",\n                \"collapsed\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"9\",\n                \"folderId\": \"8\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"w_{d}=\\\\sqrt{\\\\frac{k}{m}-\\\\frac{c^{2}}{4m^{2}}}\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"11\",\n                \"folderId\": \"8\",\n                \"color\": \"#c74440\",\n                \"latex\": \"f\\\\left(x\\\\right)=y_{0}\\\\cdot e^{-\\\\frac{c}{2m}x}\\\\left(\\\\cos\\\\left(w_{d}\\\\cdot x\\\\right)+\\\\frac{c}{2m\\\\cdot w_{d}}\\\\sin\\\\left(w_{d}\\\\cdot x\\\\right)\\\\right)\\\\left\\\\{x\\\\ge0\\\\right\\\\}\",\n                \"hidden\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"12\",\n                \"folderId\": \"8\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"g\\\\left(x\\\\right)=f\\\\left(x\\\\right)\",\n                \"hidden\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"14\",\n                \"folderId\": \"8\",\n                \"color\": \"#c74440\",\n                \"latex\": \"g\\\\left(x\\\\right)\\\\left\\\\{0\\\\le x\\\\le t_{s}\\\\right\\\\}\",\n                \"colorLatex\": \"c_{g}\",\n                \"lineWidth\": \"3\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"13\",\n                \"folderId\": \"8\",\n                \"color\": \"#c74440\",\n                \"latex\": \"\\\\left(t_{s},g\\\\left(t_{s}\\\\right)\\\\right)\",\n                \"dragMode\": \"NONE\",\n                \"colorLatex\": \"c_{g}\"\n            },\n            {\n                \"type\": \"folder\",\n                \"id\": \"17\",\n                \"title\": \"Button\",\n                \"collapsed\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"31\",\n                \"folderId\": \"17\",\n                \"color\": \"#c74440\",\n                \"latex\": \"N_{cap}=0\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"19\",\n                \"folderId\": \"17\",\n                \"text\": \"Capture:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"60\",\n                \"folderId\": \"17\",\n                \"color\": \"#c74440\",\n                \"latex\": \"p=\\\\frac{27}{140}\\\\left(x_{Rbound}-x_{Lbound}\\\\right)\",\n                \"displayEvaluationAsFraction\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"61\",\n                \"folderId\": \"17\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"d=\\\\frac{3}{140}\\\\left(x_{Rbound}-x_{Lbound}\\\\right)\",\n                \"displayEvaluationAsFraction\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"20\",\n                \"folderId\": \"17\",\n                \"color\": \"#388c46\",\n                \"latex\": \"\\\\operatorname{polygon}\\\\left(\\\\left(x_{Rbound}-d,1.9\\\\right),\\\\left(x_{Rbound}-d-p,1.9\\\\right),\\\\left(x_{Rbound}-d-p,1.6\\\\right),\\\\left(x_{Rbound}-d,1.6\\\\right)\\\\right)\",\n                \"lines\": false,\n                \"colorLatex\": \"c_{white}\",\n                \"fillOpacity\": \"1\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"24\",\n                \"folderId\": \"17\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\operatorname{polygon}\\\\left(\\\\left(x_{Rbound}-d,1.9\\\\right),\\\\left(x_{Rbound}-d-p,1.9\\\\right),\\\\left(x_{Rbound}-d-p,1.6\\\\right),\\\\left(x_{Rbound}-d,1.6\\\\right)\\\\right)\\\\left\\\\{0\\\\le N_{cap}\\\\le5\\\\right\\\\}\",\n                \"lines\": true,\n                \"fillOpacity\": \"0\",\n                \"lineWidth\": \"1.5\",\n                \"clickableInfo\": {\n                    \"enabled\": true,\n                    \"latex\": \"N_{cap}\\\\to N_{cap}+1,s_{p}\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"58\",\n                \"folderId\": \"17\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\operatorname{polygon}\\\\left(\\\\left(x_{Rbound}-d,1.9\\\\right),\\\\left(x_{Rbound}-d-p,1.9\\\\right),\\\\left(x_{Rbound}-d-p,1.6\\\\right),\\\\left(x_{Rbound}-d,1.6\\\\right)\\\\right)\\\\left\\\\{N_{cap}>5\\\\right\\\\}\",\n                \"lines\": true,\n                \"fillOpacity\": \"0\",\n                \"lineOpacity\": \".4\",\n                \"lineWidth\": \"1.5\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"25\",\n                \"folderId\": \"17\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(\\\\frac{x_{Rbound}-d+x_{Rbound}-d-p}{2},\\\\frac{1.9+1.6}{2}\\\\left\\\\{N_{cap}>5\\\\right\\\\}\\\\right)\",\n                \"showLabel\": true,\n                \"label\": \"Capture\",\n                \"hidden\": true,\n                \"labelSize\": \".8\",\n                \"pointOpacity\": \".4\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"59\",\n                \"folderId\": \"17\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(\\\\frac{x_{Rbound}-d+x_{Rbound}-d-p}{2},\\\\frac{1.9+1.6}{2}\\\\left\\\\{0\\\\le N_{cap}\\\\le5\\\\right\\\\}\\\\right)\",\n                \"showLabel\": true,\n                \"label\": \"Capture\",\n                \"hidden\": true,\n                \"labelSize\": \".8\",\n                \"pointOpacity\": \".9\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"27\",\n                \"folderId\": \"17\",\n                \"text\": \"Clear:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"28\",\n                \"folderId\": \"17\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"\\\\operatorname{polygon}\\\\left(\\\\left(x_{Rbound}-2d-p,1.9\\\\right),\\\\left(x_{Rbound}-2d-2p,1.9\\\\right),\\\\left(x_{Rbound}-2d-2p,1.6\\\\right),\\\\left(x_{Rbound}-2d-p,1.6\\\\right)\\\\right)\\\\left\\\\{N_{cap}>0\\\\right\\\\}\",\n                \"lines\": false,\n                \"colorLatex\": \"c_{white}\",\n                \"fillOpacity\": \"1\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"29\",\n                \"folderId\": \"17\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\operatorname{polygon}\\\\left(\\\\left(x_{Rbound}-2d-p,1.9\\\\right),\\\\left(x_{Rbound}-2d-2p,1.9\\\\right),\\\\left(x_{Rbound}-2d-2p,1.6\\\\right),\\\\left(x_{Rbound}-2d-p,1.6\\\\right)\\\\right)\\\\left\\\\{N_{cap}>0\\\\right\\\\}\",\n                \"lines\": true,\n                \"fillOpacity\": \"0\",\n                \"lineWidth\": \"1.5\",\n                \"clickableInfo\": {\n                    \"enabled\": true,\n                    \"latex\": \"c_{lear},N_{cap}\\\\to0\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"30\",\n                \"folderId\": \"17\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(\\\\frac{x_{Rbound}-2d-p+x_{Rbound}-2d-2p}{2},\\\\frac{1.9+1.6}{2}\\\\left\\\\{N_{cap}>0\\\\right\\\\}\\\\right)\",\n                \"showLabel\": true,\n                \"label\": \"Clear\",\n                \"hidden\": true,\n                \"labelSize\": \".8\",\n                \"pointOpacity\": \".9\"\n            },\n            {\n                \"type\": \"folder\",\n                \"id\": \"63\",\n                \"title\": \"Bound\",\n                \"collapsed\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"64\",\n                \"folderId\": \"63\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"x_{bound}=11.5\",\n                \"slider\": {\n                    \"hardMin\": true,\n                    \"hardMax\": true,\n                    \"min\": \"0.5\",\n                    \"max\": \"99.5\",\n                    \"step\": \"0.1\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"65\",\n                \"folderId\": \"63\",\n                \"color\": \"#000000\",\n                \"latex\": \"x_{Rbound}=x_{bound}+0.5\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"66\",\n                \"folderId\": \"63\",\n                \"color\": \"#c74440\",\n                \"latex\": \"x_{Lbound}=-\\\\frac{2}{12}x_{Rbound}\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"67\",\n                \"folderId\": \"63\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(x_{bound},0\\\\right)\"\n            },\n            {\n                \"type\": \"folder\",\n                \"id\": \"22\",\n                \"title\": \"Color\",\n                \"collapsed\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"23\",\n                \"folderId\": \"22\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"c_{white}=\\\\operatorname{rgb}\\\\left(255,255,255\\\\right)\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"51\",\n                \"folderId\": \"22\",\n                \"color\": \"#c74440\",\n                \"latex\": \"L_{R}=\\\\left[199,45,56,96,250\\\\right]\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"52\",\n                \"folderId\": \"22\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"L_{G}=\\\\left[68,112,140,66,126\\\\right]\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"53\",\n                \"folderId\": \"22\",\n                \"color\": \"#388c46\",\n                \"latex\": \"L_{B}=\\\\left[64,179,70,166,25\\\\right]\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"56\",\n                \"folderId\": \"22\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"c_{g}=\\\\operatorname{rgb}\\\\left(L_{R}\\\\left[M_{state}\\\\right],L_{G}\\\\left[M_{state}\\\\right],L_{B}\\\\left[M_{state}\\\\right]\\\\right)\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"57\",\n                \"folderId\": \"22\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"c_{G}=\\\\operatorname{rgb}\\\\left(L_{R}\\\\left[L_{Mstate}\\\\right],L_{G}\\\\left[L_{Mstate}\\\\right],L_{B}\\\\left[L_{Mstate}\\\\right]\\\\right)\"\n            }\n        ]\n    },\n    \"includeFunctionParametersInRandomSeed\": true,\n    \"doNotMigrateMovablePointStyle\": true,\n    \"backmigrated\": 14\n};\n\n  calculator1.setState(state1);\n  calculator2.setState(state2);\n  \n  \/\/ Source\n  var tsVar = calculator1.HelperExpression({ latex: 't_{s}' });\n  var kPar = calculator1.HelperExpression({ latex: 'k' });\n  var mPar = calculator1.HelperExpression({ latex: 'm' });\n  var cPar = calculator1.HelperExpression({ latex: 'c' });\n  var y0Par = calculator1.HelperExpression({ latex: 'y_{0}' });\n  var MsPar = calculator1.HelperExpression({ latex: 'M_{state}' });\n  var xR = calculator2.HelperExpression({ latex: 'x_{Rbound}' });\n  var xL = calculator2.HelperExpression({ latex: 'x_{Lbound}' });\n  \n  \/\/ Sink\n  tsVar.observe('numericValue', function() {\n    var value = tsVar.numericValue;\n    if (!isNaN(value)) {\n      calculator2.setExpression({ id: '3', latex: `t_{s}=${value}` });\n    }\n  });\n  kPar.observe('numericValue', function() {\n    var value = kPar.numericValue;\n    if (!isNaN(value)) {\n      calculator2.setExpression({ id: '4', latex: `k=${value}` });\n    }\n  });\n  mPar.observe('numericValue', function() {\n    var value = mPar.numericValue;\n    if (!isNaN(value)) {\n      calculator2.setExpression({ id: '5', latex: `m=${value}` });\n    }\n  });\n  cPar.observe('numericValue', function() {\n    var value = cPar.numericValue;\n    if (!isNaN(value)) {\n      calculator2.setExpression({ id: '6', latex: `c=${value}` });\n    }\n  });\n  y0Par.observe('numericValue', function() {\n    var value = y0Par.numericValue;\n    if (!isNaN(value)) {\n      calculator2.setExpression({ id: '10', latex: `y_{0}=${value}` });\n    }\n  });\n  MsPar.observe('numericValue', function() {\n    var value = MsPar.numericValue;\n    if (!isNaN(value)) {\n      calculator2.setExpression({ id: '54', latex: `M_{state}=${value}` });\n    }\n  });\n  \n  \/\/ Update graph bounds\nfunction updateBounds() {\n  var left = xL.numericValue;\n  var right = xR.numericValue;\n\n  if (!isNaN(left)) {\n    if (!isNaN(right)) {\n      calculator2.setMathBounds({\n        left: left,\n        right: right,\n        bottom: -2,\n        top: 2\n      });\n    }\n  }\n}\n\nxL.observe('numericValue', updateBounds);\nxR.observe('numericValue', updateBounds);\n  \n<\/script>\n<\/div>\n<\/div>\n\n\n\n<p>In <a href=\"#calculator2\">Visualization 2<\/a>, use &#8220;Capture&#8221; to save the current graph. You can use it to compare two or more graphs produced with different settings. Use &#8220;Clear&#8221; to remove all captured graphs. You can also adjust the horizontal-axis bounds by dragging the black point on the right side of the axis to the left or right.<\/p>\n<\/div><\/div>\n\n\n\n<h3>Ready for More?<\/h3>\n\n\n\n<p>Above, you explored how the graph of the mass&#8217;s vertical displacement over time changes under different settings. But there is more to explore! You can also investigate relationships between other quantities in the spring-mass system. Use the graphing calculator in <a href=\"#calculator3\">Visualization 3<\/a> to explore relationships between quantities of your choice. Enter values for the quantities you want to investigate in the table, and then look for patterns in the resulting graph.<\/p>\n\n\n\n<div class=\"wp-block-group alignwide\"><div class=\"wp-block-group__inner-container\">\n<div class=\"wp-block-columns alignwide\">\n<div class=\"wp-block-column\">\n<figure>\n<div id=\"calculator3\" class=\"aligncenter size-full\" style=\"width: 800px; height: 450px;\"><\/div>\n<figcaption>Visualization 3: Explore relationships between quantities of your choice<\/figcaption>\n<\/figure>\n\n<script>\n  var calculator3 = Desmos.GraphingCalculator(document.getElementById('calculator3'), {\n    settingsMenu: false\n  });\n\n  var state3 = {\n    \"version\": 11,\n    \"graph\": {\n        \"viewport\": {\n            \"xmin\": -10,\n            \"ymin\": -25.083798882681563,\n            \"xmax\": 10,\n            \"ymax\": 25.083798882681563\n        },\n        \"xAxisArrowMode\": \"POSITIVE\",\n        \"yAxisArrowMode\": \"POSITIVE\",\n        \"__v12ViewportLatexStash\": {\n            \"xmin\": \"-10\",\n            \"xmax\": \"10\",\n            \"ymin\": \"-25.083798882681563\",\n            \"ymax\": \"25.083798882681563\"\n        }\n    },\n    \"expressions\": {\n        \"list\": [\n            {\n                \"type\": \"text\",\n                \"id\": \"2\",\n                \"text\": \"Each column represents a quantity. Enter its values in the rows below.\"\n            },\n            {\n                \"id\": \"6\",\n                \"type\": \"table\",\n                \"columns\": [\n                    {\n                        \"values\": [\n                            \"\",\n                            \"\",\n                            \"\",\n                            \"\",\n                            \"\"\n                        ],\n                        \"hidden\": true,\n                        \"id\": \"4\",\n                        \"color\": \"#388c46\",\n                        \"latex\": \"x_{1}\"\n                    },\n                    {\n                        \"id\": \"5\",\n                        \"color\": \"#6042a6\",\n                        \"latex\": \"y_{1}\"\n                    }\n                ]\n            }\n        ]\n    },\n    \"includeFunctionParametersInRandomSeed\": true,\n    \"doNotMigrateMovablePointStyle\": true,\n    \"backmigrated\": 14\n};\n\n  calculator3.setState(state3);\n<\/script>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<p>As a starting point, investigate the relationship between mass and period for undamped oscillations (that is, when the damping coefficient is 0). Here, the <em>period<\/em> is the time required for the mass to complete one full cycle of its oscillation.<\/p>\n\n\n\n<blockquote class=\"wp-block-quote\"><p>What pattern do you notice? How does the period change as the mass increases? Can you use the graph to describe or predict this relationship?<\/p><\/blockquote>\n\n\n\n<p>Next, explore damped oscillations. Set the damping coefficient to a value greater than 0 and investigate how the amplitude of the oscillation changes over time. Here, the <em>amplitude<\/em> is the maximum displacement of the mass from its equilibrium position.<\/p>\n\n\n\n<blockquote class=\"wp-block-quote\"><p>What pattern do you notice? Does the amplitude decrease at a constant rate, or does the rate of decrease change over time?<\/p><\/blockquote>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<div style=\"height:100px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-group is-style-twentytwentyone-border\"><div class=\"wp-block-group__inner-container\">\n<div class=\"related-topics\">\n  <h3>Explore related topics<\/h3>\n  <p>Discover more contents with related topics in this website.<\/p>\n  <ul class=\"topics-list\">\n    <li><a href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s=Mathematics\">Mathematics<\/a><\/li>\n    <li><a href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s=Physics\">Physics<\/a><\/li>\n    <li><a href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s=Spring+Mass+Systems\">Spring-Mass Systems<\/a><\/li>\n    <li><a href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s=Oscillation\">Oscillation<\/a><\/li>\n    <li><a href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s=Graphs\">Graphs<\/a><\/li>\n    <li><a href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s=Functions\">Functions<\/a><\/li>\n    <li><a href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s=Interactive+Learning+Resource\">Interactive Learning Resource<\/a><\/li>\n  <\/ul>\n<\/div>\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>A spring can move back and forth when a mass is attached to it and pulled away from its resting position. But what determines how the mass moves, and how does changing the conditions affect its motion? In this interactive resource, you can experiment with a spring-mass system by changing different settings and observing what&hellip; <a class=\"more-link\" href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/learning-resources\/exploring-vertical-spring-mass-systems\/\">Continue reading <span class=\"screen-reader-text\">Exploring Vertical Spring-Mass Systems<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":2270,"parent":1140,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Exploring Vertical Spring-Mass Systems<\/title>\n<meta name=\"description\" content=\"Explore a vertical spring-mass system by changing parameters, observing motion, and comparing displacement-time graphs.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/learning-resources\/exploring-vertical-spring-mass-systems\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Exploring Vertical Spring-Mass Systems\" \/>\n<meta property=\"og:description\" content=\"Explore a vertical spring-mass system by changing parameters, observing motion, and comparing displacement-time graphs.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/learning-resources\/exploring-vertical-spring-mass-systems\/\" \/>\n<meta property=\"og:site_name\" content=\"Yosep Dwi Kristanto \u2014 Universitas Sanata Dharma\" \/>\n<meta property=\"article:modified_time\" content=\"2026-09-27T11:43:15+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/people.usd.ac.id\/~ydkristanto\/wp-content\/uploads\/2026\/09\/header-spring-in-motion.png\" \/>\n\t<meta property=\"og:image:width\" content=\"1200\" \/>\n\t<meta property=\"og:image:height\" content=\"600\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/png\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data1\" content=\"13 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebSite\",\"@id\":\"https:\/\/people.usd.ac.id\/~ydkristanto\/#website\",\"url\":\"https:\/\/people.usd.ac.id\/~ydkristanto\/\",\"name\":\"Yosep Dwi Kristanto \\u2014 Universitas Sanata Dharma\",\"description\":\"\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"ImageObject\",\"@id\":\"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/learning-resources\/exploring-vertical-spring-mass-systems\/#primaryimage\",\"inLanguage\":\"en-US\",\"url\":\"https:\/\/people.usd.ac.id\/~ydkristanto\/wp-content\/uploads\/2026\/09\/header-spring-in-motion.png\",\"contentUrl\":\"https:\/\/people.usd.ac.id\/~ydkristanto\/wp-content\/uploads\/2026\/09\/header-spring-in-motion.png\",\"width\":1200,\"height\":600},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/learning-resources\/exploring-vertical-spring-mass-systems\/#webpage\",\"url\":\"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/learning-resources\/exploring-vertical-spring-mass-systems\/\",\"name\":\"Exploring Vertical Spring-Mass Systems\",\"isPartOf\":{\"@id\":\"https:\/\/people.usd.ac.id\/~ydkristanto\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/learning-resources\/exploring-vertical-spring-mass-systems\/#primaryimage\"},\"datePublished\":\"2026-09-26T13:54:15+00:00\",\"dateModified\":\"2026-09-27T11:43:15+00:00\",\"description\":\"Explore a vertical spring-mass system by changing parameters, observing motion, and comparing displacement-time graphs.\",\"breadcrumb\":{\"@id\":\"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/learning-resources\/exploring-vertical-spring-mass-systems\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/learning-resources\/exploring-vertical-spring-mass-systems\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/learning-resources\/exploring-vertical-spring-mass-systems\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/people.usd.ac.id\/~ydkristanto\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Interactive Mathematics Learning Resources\",\"item\":\"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/learning-resources\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Exploring Vertical Spring-Mass Systems\"}]}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Exploring Vertical Spring-Mass Systems","description":"Explore a vertical spring-mass system by changing parameters, observing motion, and comparing displacement-time graphs.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/learning-resources\/exploring-vertical-spring-mass-systems\/","og_locale":"en_US","og_type":"article","og_title":"Exploring Vertical Spring-Mass Systems","og_description":"Explore a vertical spring-mass system by changing parameters, observing motion, and comparing displacement-time graphs.","og_url":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/learning-resources\/exploring-vertical-spring-mass-systems\/","og_site_name":"Yosep Dwi Kristanto \u2014 Universitas Sanata Dharma","article_modified_time":"2026-09-27T11:43:15+00:00","og_image":[{"width":1200,"height":600,"url":"https:\/\/people.usd.ac.id\/~ydkristanto\/wp-content\/uploads\/2026\/09\/header-spring-in-motion.png","type":"image\/png"}],"twitter_card":"summary_large_image","twitter_misc":{"Est. reading time":"13 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebSite","@id":"https:\/\/people.usd.ac.id\/~ydkristanto\/#website","url":"https:\/\/people.usd.ac.id\/~ydkristanto\/","name":"Yosep Dwi Kristanto \u2014 Universitas Sanata Dharma","description":"","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/people.usd.ac.id\/~ydkristanto\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"ImageObject","@id":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/learning-resources\/exploring-vertical-spring-mass-systems\/#primaryimage","inLanguage":"en-US","url":"https:\/\/people.usd.ac.id\/~ydkristanto\/wp-content\/uploads\/2026\/09\/header-spring-in-motion.png","contentUrl":"https:\/\/people.usd.ac.id\/~ydkristanto\/wp-content\/uploads\/2026\/09\/header-spring-in-motion.png","width":1200,"height":600},{"@type":"WebPage","@id":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/learning-resources\/exploring-vertical-spring-mass-systems\/#webpage","url":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/learning-resources\/exploring-vertical-spring-mass-systems\/","name":"Exploring Vertical Spring-Mass Systems","isPartOf":{"@id":"https:\/\/people.usd.ac.id\/~ydkristanto\/#website"},"primaryImageOfPage":{"@id":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/learning-resources\/exploring-vertical-spring-mass-systems\/#primaryimage"},"datePublished":"2026-09-26T13:54:15+00:00","dateModified":"2026-09-27T11:43:15+00:00","description":"Explore a vertical spring-mass system by changing parameters, observing motion, and comparing displacement-time graphs.","breadcrumb":{"@id":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/learning-resources\/exploring-vertical-spring-mass-systems\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/learning-resources\/exploring-vertical-spring-mass-systems\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/learning-resources\/exploring-vertical-spring-mass-systems\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/people.usd.ac.id\/~ydkristanto\/"},{"@type":"ListItem","position":2,"name":"Interactive Mathematics Learning Resources","item":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/learning-resources\/"},{"@type":"ListItem","position":3,"name":"Exploring Vertical Spring-Mass Systems"}]}]}},"_links":{"self":[{"href":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/wp-json\/wp\/v2\/pages\/2265"}],"collection":[{"href":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/wp-json\/wp\/v2\/comments?post=2265"}],"version-history":[{"count":28,"href":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/wp-json\/wp\/v2\/pages\/2265\/revisions"}],"predecessor-version":[{"id":2318,"href":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/wp-json\/wp\/v2\/pages\/2265\/revisions\/2318"}],"up":[{"embeddable":true,"href":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/wp-json\/wp\/v2\/pages\/1140"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/wp-json\/wp\/v2\/media\/2270"}],"wp:attachment":[{"href":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/wp-json\/wp\/v2\/media?parent=2265"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}