{"id":2309,"date":"2026-09-27T18:32:50","date_gmt":"2026-09-27T11:32:50","guid":{"rendered":"https:\/\/people.usd.ac.id\/~ydkristanto\/?page_id=2309"},"modified":"2026-09-27T18:52:27","modified_gmt":"2026-09-27T11:52:27","slug":"eksplorasi-sistem-pegas-massa-vertikal","status":"publish","type":"page","link":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/media-pengajaran\/eksplorasi-sistem-pegas-massa-vertikal\/","title":{"rendered":"Eksplorasi Sistem Pegas-Massa Vertikal"},"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\/learning-resources\/exploring-vertical-spring-mass-systems\/\">EN<\/a><\/div>\n<\/div>\n\n\n\n<p class=\"has-drop-cap\">Ketika sebuah massa digantungkan pada pegas dan ditarik menjauh dari posisi setimbangnya, massa itu dapat bergerak naik dan turun. Namun, apa yang menentukan bagaimana massa tersebut bergerak? Bagaimana perubahan kondisi memengaruhi gerakannya? Dalam sumber belajar interaktif ini, kamu dapat bereksperimen dengan sistem pegas-massa. <\/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\">Melihat Gerak Pegas melalui Grafik<\/h3>\n\n\n\n<p>Sesuaikan konstanta pegas, massa, redaman, dan posisi awal. Jalankan animasi dan lihat bagaimana gerakan massa pada pegas tersebut direpresentasikan dalam grafik.<\/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>Visualisasi 1: Pegas yang bergerak<\/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>Visualisasi 2: Grafik perpindahan terhadap waktu<\/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    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       \"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\": \"Mainkan\",\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\": \"Jeda\",\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\": \"Waktu (s)\",\n        \"yAxisLabel\": \"Perpindahan (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\": \"Simpan\",\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\": \"Hapus\",\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>Pada <a href=\"#calculator2\">Visualisasi 2<\/a>, gunakan &#8220;Simpan&#8221; untuk menyimpan grafik yang sedang ditampilkan. Kamu dapat menggunakannya untuk membandingkan dua atau lebih grafik yang dihasilkan dengan pengaturan yang berbeda. Gunakan &#8220;Hapus&#8221; untuk menghapus semua grafik yang telah disimpan. Kamu juga dapat mengatur batas sumbu horizontal. Caranya, geser titik hitam yang berada di sisi kanan sumbu tersebut ke kiri atau kanan.<\/p>\n<\/div><\/div>\n\n\n\n<h3>Siap untuk Eksplorasi Lebih Lanjut?<\/h3>\n\n\n\n<p>Di atas, kamu telah mengeksplorasi bagaimana grafik perpindahan vertikal sebuah massa setiap waktunya berubah ketika pengaturan sistem diubah. Namun, masih banyak hal yang dapat dieksplorasi!<\/p>\n\n\n\n<p>Kamu juga dapat menyelidiki hubungan antara berbagai kuantitas dalam sistem pegas-massa. Gunakan kalkulator grafik pada <a href=\"#calculator3\">Visualisasi 3<\/a> untuk mengeksplorasi hubungan antara kuantitas yang kamu pilih. Masukkan nilai-nilai besaran tersebut ke dalam tabel. Kemudian, amati pola yang muncul pada grafik.<\/p>\n\n\n\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>Visualisasi 3: Eksplorasi hubungan antara berbagai kuantitas<\/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\": \"Setiap kolom mewakili satu kuantitas. Masukkan nilai kuantitas tersebut pada baris-baris di bawahnya.\"\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\n\n\n<p>Sebagai langkah awal, selidikilah hubungan antara massa dan periode pada osilasi tanpa redaman (yaitu ketika koefisien redaman bernilai 0). <em>Periode<\/em> adalah waktu yang diperlukan sebuah massa untuk menyelesaikan satu siklus penuh osilasi.<\/p>\n\n\n\n<blockquote class=\"wp-block-quote\"><p>Pola apa yang kamu temukan? Bagaimana periode berubah ketika massa bertambah? Dapatkah kamu menggunakan grafik untuk menjelaskan atau memprediksi hubungan tersebut?<\/p><\/blockquote>\n\n\n\n<p>Selanjutnya, eksplorasilah osilasi teredam. Atur koefisien redaman ke nilai lebih besar dari 0. Kemudian, selidikilah bagaimana amplitudo osilasi berubah terhadap waktu. <em>Amplitudo<\/em> adalah jarak terbesar sebuah massa dari posisi setimbangnya.<\/p>\n\n\n\n<blockquote class=\"wp-block-quote\"><p>Pola apa yang kamu temukan? Apakah amplitudo berkurang dengan laju yang tetap? Atau, apakah laju pengurangannya berubah seiring waktu?<\/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>Jelajahi topik-topik terkait<\/h3>\n  <p>Temukan konten-konten terkait lainnya dalam situs web ini.<\/p>\n  <ul class=\"topics-list\">\n    <li><a href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s=Matematika\">Matematika<\/a><\/li>\n    <li><a href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s=Fisika\">Fisika<\/a><\/li>\n    <li><a href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s=Sistem+Pegas+Massa\">Sistem Pegas-Massa<\/a><\/li>\n    <li><a href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s=Osilasi\">Osilasi<\/a><\/li>\n    <li><a href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s=Grafik\">Grafik<\/a><\/li>\n    <li><a href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s=Fungsi\">Fungsi<\/a><\/li>\n    <li><a href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s=Sumber+Belajar+Interaktif\">Sumber Belajar Interaktif<\/a><\/li>\n  <\/ul>\n<\/div>\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Ketika sebuah massa digantungkan pada pegas dan ditarik menjauh dari posisi setimbangnya, massa itu dapat bergerak naik dan turun. Namun, apa yang menentukan bagaimana massa tersebut bergerak? Bagaimana perubahan kondisi memengaruhi gerakannya? Dalam sumber belajar interaktif ini, kamu dapat bereksperimen dengan sistem pegas-massa. Melihat Gerak Pegas melalui Grafik Sesuaikan konstanta pegas, massa, redaman, dan posisi&hellip; <a class=\"more-link\" href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/media-pengajaran\/eksplorasi-sistem-pegas-massa-vertikal\/\">Continue reading <span class=\"screen-reader-text\">Eksplorasi Sistem Pegas-Massa Vertikal<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":2270,"parent":882,"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>Eksplorasi Sistem Pegas-Massa Vertikal<\/title>\n<meta name=\"description\" content=\"Eksplorasi sistem pegas-massa vertikal dengan mengubah pengaturan, mengamati gerakan, dan menemukan pola melalui grafik.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" 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