Difference between revisions of "Driven oscillations of a mass on a nonlinear spring"

File "Spring.js" <syntaxhighlight lang="javascript" enclose="div">

   window.addEventListener("load", Main_Spring, true);
   function Main_Spring() {
   var canvas = spring_canvas;
   canvas.onselectstart = function () {return false;};     // prohibition selection canvas
   var ctx = canvas.getContext("2d");                      // at the ctx is drawing
   var w = canvas.width;                                   // the width of the window in the calculated coordinates
   var h = canvas.height;                                  // the height of the window in the calculated coordinates
   var Pi = 3.1415926;    	      	                    // Pi
   var m0 = 1;    		      	                    // weight scale
   var T0 = 1;    		      	                    // time scale (the period of oscillation of the original system)
   var t = 0;
   var k0 = 2 * Pi / T0;           	                    // frequency scale
   var C0 = m0 * k0 * k0;          	                    // hardness scale
   var B0 = 2 * m0 * k0;  	      	                    // viscosity scale
   var omega = 10;
   
   // *** Creating the physical parameters***
   var F = 80;
   var m = 1 * m0;                 	                    // weight
   var C = 1 * C0;                 	                    // rigidity
   var C1 = 1 * C0;                 	                    // rigidity1
   var B = .1 * B0;                 	                    // viscosity
   
   slider_m.value = (m / m0).toFixed(1); number_m.value = (m / m0).toFixed(1);
   slider_C.value = (C / C0).toFixed(1); number_C.value = (C / C0).toFixed(1);
   slider_C1.value = (C / C0).toFixed(1); number_C1.value = (C / C0).toFixed(1);
   slider_B.value = (B / B0).toFixed(1); number_B.value = (B / B0).toFixed(1);
   slider_F.value = (F / 40).toFixed(1); number_F.value = (F / 40).toFixed(1);

   // *** Creating the parameters of computing ***

   var fps = 300;		      	            // frames per second
   var spf = 100;		      	            // steps per frame 
   var dt  = 0.05 * T0 / fps;    	            // integration step (calculation quality) 
   var steps = 0;                                  // the number of integration steps

   function setM(new_m) {m = new_m * m0;}
   function setC(new_C) {C = new_C * C0;}
   function setC1(new_C1) {C1 = new_C1 * C0 * 0.067;}
   function setB(new_B) {B = new_B * B0;}
   function setF(new_F) {F = new_F * 40;}

   slider_m.oninput = function() {number_m.value = slider_m.value;       setM(slider_m.value);};
   number_m.oninput = function() {slider_m.value = number_m.value;       setM(number_m.value);};
   slider_C.oninput = function() {number_C.value = slider_C.value;       setC(slider_C.value);};
   number_C.oninput = function() {slider_C.value = number_C.value;       setC(number_C.value);};
   slider_C1.oninput = function() {number_C1.value = slider_C1.value;       setC1(slider_C1.value);};
   number_C1.oninput = function() {slider_C1.value = number_C1.value;       setC1(number_C1.value);};
   slider_B.oninput = function() {number_B.value = slider_B.value;       setB(slider_B.value);};
   number_B.oninput = function() {slider_B.value = number_B.value;       setB(number_B.value);};
   slider_F.oninput = function() {number_F.value = slider_F.value;       setF(slider_F.value);};
   number_F.oninput = function() {slider_F.value = number_F.value;       setF(number_F.value);};

   var count = true;                   // system analysis
   var v = 0;				// cargo speed

   var rw = canvas.width / 30;    	
   var rh = canvas.height / 1.5;
   var x0 = 15 * rw - rw / 2;     	
   var y0 = rh / 1.33 - rh / 2;

   // spring settings
   var coil = 10;        // number of turns
   var startX = 0;       // spring fastening

   // create a rectangle-cargo
   var rect = {
       x: x0,  width: rw,
       y: y0,	height: rh,
       fill: "rgba(0, 0, 255, 1)"    	// colour
   };

   // capture a rectangle with the mouse
   var mx_;                                    // буфер позиции мыши (для расчета скорости при отпускании шара)
   document.onmousedown = function(e) {        // function by pressing the mouse button
       var m = mouseCoords(e);                 // we get estimated coordinates of the mouse cursor
       var x = rect.x;
       var xw = rect.x + rect.width;
       var y = rect.y;
       var yh = rect.y + rect.height;
       if (x <= m.x && xw >= m.x   && y <= m.y && yh >= m.y) {
           if (e.which == 1) {                         // left mouse button is pressed
               rect.xPlus = rect.x - m.x;              // cursor shift relative to the cargo on the x
               rect.yPlus = rect.y - m.y;              // cursor shift relative to the cargo on the y
               mx_ = m.x;
               count = false;
               document.onmousemove = mouseMove;       // while a key is pressed, fanction of motions is correct
           }
       }
   };

   document.onmouseup = function(e) {          // function when you release the mouse button
       document.onmousemove = null;              // when the key is released, no movement function
       count = true;
   };

   function mouseMove(e) {                     // function when you move the mouse, it works only while holding LKM
       var m = mouseCoords(e);                 // we get estimated coordinates of the mouse cursor
       rect.x = m.x + rect.xPlus;

// v = 6.0 * (m.x - mx_) / dt / fps; // inertia preservation

       v = 0;
       mx_ = m.x;
   }

   function mouseCoords(e) {                   // function returns the calculated coordinates of the mouse cursor
       var m = [];
       var rect = canvas.getBoundingClientRect();
       m.x = (e.clientX - rect.left);
       m.y = (e.clientY - rect.top);
       return m;
   }

   // plot
   var vGraph = new TM_graph(                  // determine the plot
       "#vGraph",                              // on html-element #vGraph
       250,                                    // the number of steps by "x" axis
       -1, 1, 0.2);                            // min value of Y-axis, max value of Y-axis, Y-axis step

   function control() {
       calculate();
       draw();
       requestAnimationFrame(control);
   }
   control();

// setInterval(control, 1000 / fps); // starting system

   function calculate() {
       if (!count) return;
       for (var s=1; s<=spf; s++) {
           var f = -B*v - C * (rect.x - x0) - C1*Math.pow(rect.x - x0,3)+2*F*Math.sin(t);

v += f / m * dt; //console.log(f);

           rect.x += v * dt;

t+= dt;

           steps++;
           if (steps % 80 == 0) vGraph.graphIter(steps, (rect.x-x0)/canvas.width*2);   // infeed graph data
       }

   }

   function draw() {
       ctx.clearRect(0, 0, w, h);

draw_spring(startX, rect.x, h/2, 10, 50);

       ctx.fillStyle = "#0000ff";
       ctx.fillRect(rect.x, rect.y, rect.width, rect.height);
   }

function draw_spring(x_start, x_end, y, n, h) { ctx.lineWidth = 2;

       ctx.strokeStyle = "#7394cb";

var L = x_end - x_start; for (var i = 0; i < n; i++) { var x_st = x_start + L / n * i; var x_end = x_start + L / n * (i + 1); var l = x_end - x_st; ctx.beginPath(); ctx.bezierCurveTo(x_st, y, x_st + l / 4, y + h, x_st + l / 2, y); ctx.bezierCurveTo(x_st + l / 2, y, x_st + 3 * l / 4, y - h, x_st + l, y); ctx.stroke(); } }