Problem 3-3

problem3-1.html

@@ -154,26 +154,6 @@
             ctx.beginPath();
             ctx.arc(xPos - 20, yPos - (100 - y1), Math.PI * Math.sqrt(m1), 0, Math.PI * 2);
             ctx.fill();
-            /*ctx.beginPath();
-            ctx.arc(xPos + lx / 2, yPos, pulleyR, 0, Math.PI * 2);
-            ctx.stroke();
-            ctx.beginPath();
-            ctx.arc(xPos - lx / 2, yPos, pulleyR, 0, Math.PI * 2);
-            ctx.stroke();
-            ctx.beginPath();
-            ctx.moveTo(xPos + lx / 2 + pulleyR, yPos);
-            ctx.lineTo(xPos + lx / 2 + pulleyR + r * Math.sin(theta), yPos - r * Math.cos(theta));
-            ctx.stroke();
-            ctx.beginPath();
-            ctx.moveTo(xPos - lx / 2 - pulleyR, yPos);
-            ctx.lineTo(xPos - lx / 2 - pulleyR, yPos - (250 - r));
-            ctx.stroke();
-            ctx.beginPath();
-            ctx.arc(xPos + lx / 2 + pulleyR + r * Math.sin(theta), yPos - r * Math.cos(theta), 5, 0, Math.PI * 2);
-            ctx.fill();
-            ctx.beginPath();
-            ctx.arc(xPos - lx / 2 - pulleyR, yPos - (250 - r), 5, 0, Math.PI * 2);
-            ctx.fill();*/
         }
 
 

problem3-2.html

@@ -91,10 +91,10 @@
         calcAccelerations();
         //Relative position of canvas
         var xPos = 0;
-        var yPos = 70;
+        var yPos = 90;
         //Moves and scales canvas
         ctx.translate(ctx.canvas.width / 2, ctx.canvas.height / 2)
-        ctx.scale(2, -2);
+        ctx.scale(1.5, -1.5);
 
         function calcAccelerations()
         {
@@ -144,15 +144,15 @@
             {
                 Reset();
             }
-            if (75 - y2 - y1 <= 20)
+            if (100 - y2 - y1 <= 20)
             {
                 Reset();
             }
-            if (75 - y3 - y1 <= 20)
+            if (100 - y3 - y1 <= 20)
             {
                 Reset();
             }
-            if (75 + y1 <= 35)
+            if (100 + y1 <= 35)
             {
                 Reset();
             }
@@ -176,52 +176,32 @@
             ctx.stroke();
             ctx.beginPath();
             ctx.moveTo(xPos - 20, yPos);
-            ctx.lineTo(xPos - 20, yPos - (75 - y1));
+            ctx.lineTo(xPos - 20, yPos - (100 - y1));
             ctx.stroke();
             ctx.beginPath();
-            ctx.arc(xPos - 20, yPos - (75 - y1), Math.PI * Math.sqrt(m1), 0, Math.PI * 2);
+            ctx.arc(xPos - 20, yPos - (100 - y1), Math.PI * Math.sqrt(m1), 0, Math.PI * 2);
             ctx.fill();
             ctx.beginPath();
             ctx.moveTo(xPos + 20, yPos);
-            ctx.lineTo(xPos + 20, yPos - (75 + y1));
+            ctx.lineTo(xPos + 20, yPos - (100 + y1));
             ctx.stroke();
             ctx.beginPath();
-            ctx.arc(xPos + 20, yPos - (75 + y1), 20, 0, Math.PI * 2);
+            ctx.arc(xPos + 20, yPos - (100 + y1), 20, 0, Math.PI * 2);
             ctx.stroke();
             ctx.beginPath();
-            ctx.moveTo(xPos, yPos - (75 + y1));
+            ctx.moveTo(xPos, yPos - (100 + y1));
-            ctx.lineTo(xPos, yPos - (150 - y2));
+            ctx.lineTo(xPos, yPos - (200 - y2));
             ctx.stroke();
             ctx.beginPath();
-            ctx.arc(xPos, yPos - (150 - y2), Math.PI * Math.sqrt(m2), 0, Math.PI * 2);
+            ctx.arc(xPos, yPos - (200 - y2), Math.PI * Math.sqrt(m2), 0, Math.PI * 2);
             ctx.fill();
             ctx.beginPath();
-            ctx.moveTo(xPos + 40, yPos - (75 + y1));
+            ctx.moveTo(xPos + 40, yPos - (100 + y1));
-            ctx.lineTo(xPos + 40, yPos - (150 - y3));
+            ctx.lineTo(xPos + 40, yPos - (200 - y3));
             ctx.stroke();
             ctx.beginPath();
-            ctx.arc(xPos + 40, yPos - (150 - y3), Math.PI * Math.sqrt(m3), 0, Math.PI * 2);
+            ctx.arc(xPos + 40, yPos - (200 - y3), Math.PI * Math.sqrt(m3), 0, Math.PI * 2);
             ctx.fill();
-            /*ctx.beginPath();
-            ctx.arc(xPos + lx / 2, yPos, pulleyR, 0, Math.PI * 2);
-            ctx.stroke();
-            ctx.beginPath();
-            ctx.arc(xPos - lx / 2, yPos, pulleyR, 0, Math.PI * 2);
-            ctx.stroke();
-            ctx.beginPath();
-            ctx.moveTo(xPos + lx / 2 + pulleyR, yPos);
-            ctx.lineTo(xPos + lx / 2 + pulleyR + r * Math.sin(theta), yPos - r * Math.cos(theta));
-            ctx.stroke();
-            ctx.beginPath();
-            ctx.moveTo(xPos - lx / 2 - pulleyR, yPos);
-            ctx.lineTo(xPos - lx / 2 - pulleyR, yPos - (250 - r));
-            ctx.stroke();
-            ctx.beginPath();
-            ctx.arc(xPos + lx / 2 + pulleyR + r * Math.sin(theta), yPos - r * Math.cos(theta), 5, 0, Math.PI * 2);
-            ctx.fill();
-            ctx.beginPath();
-            ctx.arc(xPos - lx / 2 - pulleyR, yPos - (250 - r), 5, 0, Math.PI * 2);
-            ctx.fill();*/
         }
 
 
@@ -229,7 +209,7 @@
             c.width = window.innerWidth;
             c.height = window.innerHeight;
             ctx.translate(c.width / 2, c.height / 2);
-            ctx.scale(2, -2);
+            ctx.scale(1.5, -1.5);
         }, true);
 
         Update();

problem3-3.html

@@ -0,0 +1,139 @@
+<!--
+    This work is licensed under CC BY-NC-ND 4.0            
+    Link to license: http://creativecommons.org/licenses/by-nc-nd/4.0/
+    Attribute to Russell Georgi
+-->
+<html>
+    <head>
+        <title>
+            Problem 3-3
+        </title>
+        <style>
+            html, body {
+                width:  100%;
+                height: 100%;
+                margin: 0px;
+                border: 0;
+                overflow: hidden;
+                display: block;
+            }
+
+            canvas {
+                position: absolute;
+            }
+        </style>
+    </head>
+    <body>       
+        <canvas id="myCanvas" width="1" height="1" style="border:1px solid #ffffff;">
+        Your browser does not support the HTML5 canvas tag.</canvas>
+        
+        <script>
+        var c = document.getElementById("myCanvas");
+        var ctx = c.getContext("2d");
+        c.width = window.innerWidth;
+        c.height = window.innerHeight;
+        //Time step
+        var dt = 0.002;
+        var t = 0;
+        var g = 200;
+        var n = 10;
+        var positions = new Array(n);
+        var velocities = new Array(n);
+        var accelerations = new Array(n);
+        //Relative position of canvas
+        var xPos = 0;
+        var yPos = 200;
+        var dist = 75;
+        //Moves and scales canvas
+        ctx.translate(ctx.canvas.width / 2, ctx.canvas.height / 2)
+        ctx.scale(1, -1);
+
+        function Reset()
+        {
+            for (i = 0; i < n; i++)
+            {
+                positions[i] = 0;
+                velocities[i] = 0;
+                accelerations[i] = g * (2 * (2 ** i) - 1) / (2 * (2 ** i));
+            }
+        }
+        Reset();
+
+        function Clear(ctx)
+        {
+            ctx.clearRect(-c.width, -c.height, c.width * 2, c.height * 2);
+        }
+
+        function Update()
+        {
+            Clear(ctx);
+            Draw();
+            t += dt;
+            if (t > 0.7)
+            {
+                Reset();
+            }
+            for (i = 0; i < n; i++)
+            {
+                velocities[i] += accelerations[i] * dt;
+                positions[i] += velocities[i] * dt;
+            }
+            setTimeout(Update, 1000/60);
+        }
+    
+        function Draw()
+        {
+            for (i = 0; i < n; i++)
+            {
+                if (i == 0)
+                {
+                    ctx.beginPath();
+                    ctx.arc(xPos + 20 * i, yPos - dist * i, 20, 0, Math.PI * 2);
+                    ctx.stroke();
+                    ctx.beginPath();
+                    ctx.moveTo(xPos + 20 * i - 20, yPos - dist * i);
+                    ctx.lineTo(xPos + 20 * i - 20, yPos - dist * i - dist + positions[i]);
+                    ctx.stroke();
+                    ctx.beginPath();
+                    ctx.moveTo(xPos + 20 * i + 20, yPos - dist * i);
+                    ctx.lineTo(xPos + 20 * i + 20, yPos - dist * i - dist - positions[i]);
+                    ctx.stroke();
+                    ctx.beginPath();
+                    ctx.arc(xPos + 20 * i - 20, yPos - dist * i - dist + positions[i], 5, 0, Math.PI * 2);
+                    ctx.fill();
+                } else
+                {
+                    ctx.beginPath();
+                    ctx.arc(xPos + 20 * i, yPos - dist * i - positions[i - 1], 20, 0, Math.PI * 2);
+                    ctx.stroke();
+                    ctx.beginPath();
+                    ctx.moveTo(xPos + 20 * i - 20, yPos - dist * i - positions[i - 1]);
+                    ctx.lineTo(xPos + 20 * i - 20, yPos - dist * i - dist - positions[i - 1] + positions[i]);
+                    ctx.stroke();
+                    ctx.beginPath();
+                    ctx.moveTo(xPos + 20 * i + 20, yPos - dist * i - positions[i - 1]);
+                    ctx.lineTo(xPos + 20 * i + 20, yPos - dist * i - dist - positions[i]);
+                    ctx.stroke();
+                    ctx.beginPath();
+                    ctx.arc(xPos + 20 * i - 20, yPos - dist * i - dist - positions[i - 1] + positions[i], 5, 0, Math.PI * 2);
+                    ctx.fill();
+                }
+            }
+        }
+
+
+        window.addEventListener('resize', function(event) {
+            c.width = window.innerWidth;
+            c.height = window.innerHeight;
+            ctx.translate(c.width / 2, c.height / 2);
+            ctx.scale(1, -1);
+        }, true);
+
+        Update();
+
+        </script>
+    </body>
+    <p xmlns:cc="http://creativecommons.org/ns#" style="font-size: 1vw; bottom: 0px; position: absolute;">
+        This work is licensed under 
+        <a href="http://creativecommons.org/licenses/by-nc-nd/4.0/?ref=chooser-v1" target="_blank" rel="license noopener noreferrer" style="display:inline-block;">CC BY-NC-ND 4.0<img style="height:22px!important;margin-left:3px;vertical-align:text-bottom;" src="https://mirrors.creativecommons.org/presskit/icons/cc.svg?ref=chooser-v1"><img style="height:22px!important;margin-left:3px;vertical-align:text-bottom;" src="https://mirrors.creativecommons.org/presskit/icons/by.svg?ref=chooser-v1"><img style="height:22px!important;margin-left:3px;vertical-align:text-bottom;" src="https://mirrors.creativecommons.org/presskit/icons/nc.svg?ref=chooser-v1"><img style="height:22px!important;margin-left:3px;vertical-align:text-bottom;" src="https://mirrors.creativecommons.org/presskit/icons/nd.svg?ref=chooser-v1"></a></p>
+</html>