Interactive harmonic oscillator model

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Virtual laboratory > Interactive harmonic oscillator model

You can drag right or left a mass on a spring to start the oscillations:

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Download Spring_v2-1_release.zip.

The program text in the language JavaScript (Developers D.V. Tsvetkov, A.M. Krivtsov)

File "Spring.js"

  1 window.addEventListener("load", Main_Spring, true);
  2 function Main_Spring() {
  3 
  4     var canvas = spring_canvas;
  5     canvas.onselectstart = function () {return false;};     // cancel canvas selection
  6     var ctx = canvas.getContext("2d");                      // Drawing takes place in the ctx
  7     var w = canvas.width;                                   // the width of the window in the estimated coordinates
  8     var h = canvas.height;                                  // the height of the window in the estimated coordinates
  9 
 10     var Pi = 3.1415926;    	      	    // the number "PI"
 11 
 12     var m0 = 1;    		      	        // weight scale
 13     var T0 = 1;    		      	        // the time scale 
 14 
 15     var k0 = 2 * Pi / T0;           	// frequency scale
 16     var C0 = m0 * k0 * k0;          	// hardness scale
 17     var B0 = 2 * m0 * k0;  	      	    // viscosity scale
 18 
 19     // *** Assignment of physical parameters ***
 20 
 21     var m = 1 * m0;                 	// weight
 22     var C = 1 * C0;                 	// stiffness
 23     var B = .1 * B0;                 	// viscosity
 24     slider_m.value = (m / m0).toFixed(1); number_m.value = (m / m0).toFixed(1);
 25     slider_C.value = (C / C0).toFixed(1); number_C.value = (C / C0).toFixed(1);
 26     slider_B.value = (B / B0).toFixed(1); number_B.value = (B / B0).toFixed(1);
 27 
 28     // *** Assignment the parameters of computing ***
 29 
 30     var fps = 60;		      	        // frames per second - the number of frames per second 
 31     var spf = 10;		      	        // steps per frame   - the number of integration steps between frames 
 32     var dt  = 0.05 * T0 / fps;    	    // the step of integration 
 33     var steps = 0;                      // the number of integration steps
 34     function setM(new_m) {m = new_m * m0;}
 35     function setC(new_C) {C = new_C * C0;}
 36     function setB(new_B) {B = new_B * B0;}
 37 
 38     slider_m.oninput = function() {number_m.value = slider_m.value;       setM(slider_m.value);};
 39     number_m.oninput = function() {slider_m.value = number_m.value;       setM(number_m.value);};
 40     slider_C.oninput = function() {number_C.value = slider_C.value;       setC(slider_C.value);};
 41     number_C.oninput = function() {slider_C.value = number_C.value;       setC(number_C.value);};
 42     slider_B.oninput = function() {number_B.value = slider_B.value;       setB(slider_B.value);};
 43     number_B.oninput = function() {slider_B.value = number_B.value;       setB(number_B.value);};
 44 
 45     var count = true;       // whether or not the calculation of a system
 46     var v = 0;				// the speed of the body
 47 
 48     var rw = canvas.width / 30;    	var rh = canvas.height / 1.5;
 49     var x0 = 15 * rw - rw / 2;     	var y0 = rh / 1.33 - rh / 2;
 50 
 51     // the parameters of the spring
 52     var coil = 10;        // the number of turns
 53     var startX = 0;       // fixing springs
 54 
 55     // create a rectangle
 56     var rect = {
 57         x: x0,  width: rw,
 58         y: y0,	height: rh,
 59         fill: "rgba(0, 0, 255, 1)"    	// color
 60 
 61     };
 62 
 63     // capture the rectangle with the mouse
 64     var mx_;                                    // the buffer position of the mouse 
 65     document.onmousedown = function(e) {        // function by pressing the mouse button
 66         var m = mouseCoords(e);                 // received the estimated coordinates of the mouse cursor
 67 
 68         var x = rect.x;
 69         var xw = rect.x + rect.width;
 70         var y = rect.y;
 71         var yh = rect.y + rect.height;
 72         if (x <= m.x && xw >= m.x   && y <= m.y && yh >= m.y) {
 73             if (e.which == 1) {                         // Left mouse button is pressed
 74                 rect.xPlus = rect.x - m.x;              // cursor shift relative to the sinker on the x
 75                 rect.yPlus = rect.y - m.y;              // cursor shift relative to the sinker on the y
 76                 mx_ = m.x;
 77                 count = false;
 78                 document.onmousemove = mouseMove;       // until a key is pressed - is working on the movement
 79             }
 80         }
 81     };
 82 
 83     document.onmouseup = function(e) {          // function when you release the mouse button
 84         document.onmousemove = null;              // when the key is released - no movement function
 85         count = true;
 86     };
 87 
 88     function mouseMove(e) {                     // function when you move the mouse , it works only with the left mouse button 
 89         var m = mouseCoords(e);                 // received the estimated coordinates of the mouse cursor
 90         rect.x = m.x + rect.xPlus;
 91 //        v = 6.0 * (m.x - mx_) / dt / fps;     // the preservation of inertia
 92         v = 0;
 93         mx_ = m.x;
 94     }
 95 
 96     function mouseCoords(e) {                   // the function returns the calculated coordinates of the mouse cursor
 97         var m = [];
 98         var rect = canvas.getBoundingClientRect();
 99         m.x = (e.clientX - rect.left);
100         m.y = (e.clientY - rect.top);
101         return m;
102     }
103 
104     // график
105     var vGraph = new TM_graph(                  // determine the timetable
106         "#vGraph",                              // on html- element #vGraph
107         250,                                    // how many steps on the "x" axis shows
108         -1, 1, 0.2);                            // min. value of Y -axis , max . value of Y -axis , Y -axis step
109 
110     function control() {
111         calculate();
112         draw();
113         requestAnimationFrame(control);
114     }
115     control();
116 //    setInterval(control, 1000 / fps);                       // Starting system
117 
118     function calculate() {
119         if (!count) return;
120         for (var s=1; s<=spf; s++) {
121             var f =  - C * (rect.x - x0) - B * v;
122             v += f / m * dt;
123             rect.x += v * dt;
124 
125             steps++;
126             if (steps % 80 == 0) vGraph.graphIter(steps, (rect.x-x0)/canvas.width*2);   // submit the data on a graph
127         }
128 
129     }
130 
131     function draw() {
132         ctx.clearRect(0, 0, w, h);
133 
134         ctx.strokeStyle = "#0aa";
135         ctx.beginPath();
136         ctx.moveTo(0, y0+rh/2);
137         for (var i = 1; i <= coil + 1; i++ ) {
138             var x;
139             var y;
140             if (i != coil + 1) {
141                 x = startX + ((rect.x - startX))/coil*i - ((rect.x - startX))/coil/2;
142                 y = y0+rh/2 + ((i%2==0)?1:-1)*30;
143             } else {
144                 x = startX + ((rect.x - startX))/coil*i - ((rect.x - startX))/coil;
145                 y = y0+rh/2;
146             }
147 
148             ctx.lineTo(x, y);
149         }
150         ctx.stroke();
151 
152         ctx.fillStyle = "#0000ff";
153         ctx.fillRect(rect.x, rect.y, rect.width, rect.height);
154     }
155 }

Файл "Spring.html"

 1 <!DOCTYPE html>
 2 <html>
 3 <head>
 4     <meta charset="UTF-8" />
 5     <title>Пружина</title>
 6     <script src="Spring.js"></script>
 7     <script src="jquery.min.js"></script>
 8     <script src="jquery.flot.js"></script>
 9     <script src="TM_v2-1.js"></script>
10 </head>
11 <body>
12     <canvas id="spring_canvas" width="600" height="100" style="border:1px solid #000000;"></canvas><br>
13     <input type="range" id="slider_m" min="0.01" max="10" step=0.01 style="width: 150px;" />
14     m = <input type="number" id="number_m" min="0.01" max="10" step=0.01 style="width: 50px;" /><br>
15     <input type="range" id="slider_C" min="0" max="10" step=0.01 style="width: 150px;" />
16     C = <input type="number" id="number_C" min="0" max="10" step=0.01 style="width: 50px;" /><br>
17     <input type="range" id="slider_B" min="0" max="10" step=0.01 style="width: 150px;" />
18     B = <input type="number" id="number_B" min="0" max="10" step=0.01 style="width: 50px;" /><br><br>
19 
20     <table>
21         <tr><td>x</td>
22             <td><div id="vGraph" style="width:600px; height:300px; clear:both;"></div></td>
23         </tr>
24         <tr><td></td><td style="text-align: center">steps</td></tr>
25     </table>
26 </body>
27 </html>