From deda6ebd1874fe1dbd37b45da52b6c399b38ddfa Mon Sep 17 00:00:00 2001
From: rgeorgi <russellgeorgi@gmail.com>
Date: Tue, 28 Sep 2021 18:48:30 -0700
Subject: [PATCH] 5-23 and 5-29

---
 5-23.html | 167 +++++++++++++++++++++++++++++++++++++++++++
 5-29.html | 206 ++++++++++++++++++++++++++++++++++++++++++++++++++++++
 2 files changed, 373 insertions(+)
 create mode 100644 5-23.html
 create mode 100644 5-29.html
diff --git a/5-23.html b/5-23.html
new file mode 100644
index 0000000..6c65987
--- /dev/null
+++ b/5-23.html
@@ -0,0 +1,167 @@
+<!--
+    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 5-23
+        </title>
+        <style>
+            html, body {
+                width:  100%;
+                height: 100%;
+                margin: 0px;
+                border: 0;
+                overflow: hidden;
+                display: block;
+            }
+
+            canvas {
+                position: absolute;
+            }
+
+                        
+            .dropbtn {
+              background-color: #04AA6D;
+              color: white;
+              padding: 16px;
+              font-size: 16px;
+              border: none;
+            }
+
+            .dropbtnm {
+              background-color: #04AA6D;
+              color: white;
+              padding: 16px;
+              font-size: 16px;
+              border: none;
+            }
+            
+            .dropdown {
+              position: absolute;
+              display: inline-block;
+            }
+            
+            .dropdown-content {
+              display: none;
+              position: relative;
+              background-color: #f1f1f1;
+              box-shadow: 0px 8px 16px 0px rgba(0,0,0,0.2);
+              z-index: 1;
+            }
+            
+            .dropdown-content button {
+              color: black;
+              padding: 12px 16px;
+              width: 100px;
+              text-decoration: none;
+              display: block;
+            }
+
+            #m {
+                left: 110px;
+            }
+            
+            .dropdown-content a:hover {background-color: #ddd;}
+            
+            .dropdown:hover .dropdown-content {display: block;}
+            
+            .dropdown:hover .dropbtn {background-color: #3e8e41;}
+        </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");
+        ctx.canvas.width = window.innerWidth;
+        ctx.canvas.height = window.innerHeight;
+        var n = 10;
+        var g = 20;
+        var h = 55;
+        var r1 = 50;
+        var rf = 0.25;
+        var dr = 0.2;
+        var drc = 0.1;
+        var ballPositions = new Array(n);
+        var ballVelocities = new Array(n);
+        var t = 0;
+        var dt = 0.025;
+        var xPos = 0;
+        var yPos = -200;
+
+        ctx.translate(ctx.canvas.width / 2, ctx.canvas.height / 2);
+        ctx.scale(1.5, -1.5);
+        ballPositions[0] = h;
+        ballVelocities[0] = 0;
+        for (i = 1; i < ballPositions.length; i++)
+        {
+            ballPositions[i] = ballPositions[i-1] + (rf ** (i-1)) * r1 + (rf ** i) * r1 + dr;
+            ballVelocities[i] = 0;
+        }
+
+
+        function Clear(ctx)
+        {
+            ctx.clearRect(-c.width, -c.height, c.width * 2, c.height * 2);
+        }
+
+        function Update()
+        {
+            Clear(ctx);
+            Draw();
+            t += dt;
+            for (i = 0; i < ballPositions.length; i++)
+            {
+                ballVelocities[i] -= g * dt;
+                ballPositions[i] += ballVelocities[i] * dt;       
+            }
+            for (i = 0; i < ballPositions.length; i++)
+            {
+                if (i == 0 && ballPositions[i] - r1 < drc)
+                {
+                    ballVelocities[i] = -ballVelocities[i];
+                    ballPositions[i] += ballVelocities[i] * dt;  
+                } else if (i != 0 && ballPositions[i] - r1 * (rf ** i) < ballPositions[i - 1] + r1 * (rf ** (i - 1)) + drc)
+                {
+                    ballVelocities[i] = -ballVelocities[i] + 2 * ballVelocities[i - 1];
+                    ballPositions[i] += ballVelocities[i] * dt;  
+                }
+            }
+            setTimeout(Update, 1000/60)
+        }
+
+
+        function Draw()
+        {
+            ctx.beginPath();
+            ctx.moveTo(-c.width, yPos);
+            ctx.lineTo(c.width, yPos);
+            ctx.stroke();
+            for (i = 0; i < ballPositions.length; i++)
+            {
+                ctx.beginPath();
+                ctx.arc(0, ballPositions[i] + yPos, r1 * (rf ** i), 0, Math.PI * 2);
+                ctx.stroke();
+            }
+        }
+
+        window.addEventListener('resize', function(event) {
+            c.width = window.innerWidth;
+            c.height = window.innerHeight;
+            ctx.translate(c.width / 2, c.height / 2);
+            ctx.scale(1.5, -1.5);
+        }, 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> 
\ No newline at end of file
diff --git a/5-29.html b/5-29.html
new file mode 100644
index 0000000..6e71370
--- /dev/null
+++ b/5-29.html
@@ -0,0 +1,206 @@
+<!--
+    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 5-29
+        </title>
+        <style>
+            html, body {
+                width:  100%;
+                height: 100%;
+                margin: 0px;
+                border: 0;
+                overflow: hidden;
+                display: block;
+            }
+
+            canvas {
+                position: absolute;
+            }
+
+                        
+            .dropbtn {
+              background-color: #04AA6D;
+              color: white;
+              padding: 16px;
+              font-size: 16px;
+              border: none;
+            }
+
+            .dropbtnm {
+              background-color: #04AA6D;
+              color: white;
+              padding: 16px;
+              font-size: 16px;
+              border: none;
+            }
+            
+            .dropdown {
+              position: absolute;
+              display: inline-block;
+            }
+            
+            .dropdown-content {
+              display: none;
+              position: relative;
+              background-color: #f1f1f1;
+              box-shadow: 0px 8px 16px 0px rgba(0,0,0,0.2);
+              z-index: 1;
+            }
+            
+            .dropdown-content button {
+              color: black;
+              padding: 12px 16px;
+              width: 100px;
+              text-decoration: none;
+              display: block;
+            }
+
+            #m {
+                left: 110px;
+            }
+            
+            .dropdown-content a:hover {background-color: #ddd;}
+            
+            .dropdown:hover .dropdown-content {display: block;}
+            
+            .dropdown:hover .dropbtn {background-color: #3e8e41;}
+        </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>
+            class Vector2 {
+            constructor (x, y) {
+                this.x = x;
+                this.y = y;
+            }
+
+            scale(n)
+            {
+                this.x *= n;
+                this.y *= n;
+            }
+
+            get len()
+            {
+                return this.calcLen();
+            }
+
+            calcLen()
+            {
+                return (Math.sqrt(this.x * this.x + this.y * this.y));
+            }
+        }
+        var c = document.getElementById("myCanvas");
+        var ctx = c.getContext("2d");
+        ctx.canvas.width = window.innerWidth;
+        ctx.canvas.height = window.innerHeight;
+        var l = 100;
+        var r = 50;
+        var ppl = 2.0;
+        var g = 10;
+        var n = 500;
+        //var f = 1;
+        var chainPositions = new Array(1);
+        var chainPrevPositions = new Array(1);
+        var t = 0;
+        var dt = 0.0125;
+        var xPos = 0;
+        var yPos = 100;
+
+        ctx.translate(ctx.canvas.width / 2, ctx.canvas.height / 2);
+        ctx.scale(1.5, -1.5);
+        chainPositions[0] = new Vector2(r, 0);
+        chainPrevPositions[0] = new Vector2(r, 0);
+        for (i = ppl; i < r * Math.PI; i += ppl)
+        {
+            chainPositions.push(new Vector2(r * Math.cos(i / r), -r * Math.sin(i / r)));
+            chainPrevPositions.push(new Vector2(r * Math.cos(i / r), -r * Math.sin(i / r)));
+        }
+        for (i = 0; i < l; i += ppl)
+        {
+            chainPositions.push(new Vector2(-r, i));
+            chainPrevPositions.push(new Vector2(-r, i));
+        }
+
+
+        function Clear(ctx)
+        {
+            ctx.clearRect(-c.width, -c.height, c.width * 2, c.height * 2);
+        }
+
+        function Update()
+        {
+            Clear(ctx);
+            Draw();
+            t += dt;
+            for (i = 1; i < chainPositions.length; i++)
+            {
+                positionBeforeUpdate = chainPositions[i];
+                chainPositions[i] = new Vector2(2 * chainPositions[i].x - chainPrevPositions[i].x, 2 * chainPositions[i].y - chainPrevPositions[i].y);
+                chainPositions[i].y -= g * dt * dt;
+                chainPrevPositions[i] = positionBeforeUpdate;
+                /*stickCentre = new Vector2((chainPositions[i - 1].x + chainPositions[i].x) / 2, (chainPositions[i - 1].y + chainPositions[i].y) / 2);
+                stickDir = new Vector2(chainPositions[i - 1].x - chainPositions[i].x, chainPositions[i - 1].y - chainPositions[i].y);
+                stickDir = new Vector2(stickDir.x / stickDir.calcLen(), stickDir.y / stickDir.calcLen());
+                if (i != 1)
+                {
+                    chainPositions[i - 1] = new Vector2(stickCentre.x + stickDir.x * ppl / 2, stickCentre.y + stickDir.y * ppl / 2);
+                }
+                chainPositions[i] = new Vector2(stickCentre.x - stickDir.x * ppl / 2, stickCentre.y - stickDir.y * ppl / 2);*/
+            }
+            for (j = 0; j < n; j++)
+            {
+                //i = Math.floor(Math.random()*(chainPositions.length - 1));
+                i = j % (chainPositions.length - 1);
+                stickCentre = new Vector2((chainPositions[i].x + chainPositions[i + 1].x) / 2, (chainPositions[i].y + chainPositions[i + 1].y) / 2);
+                stickDir = new Vector2(chainPositions[i].x - chainPositions[i + 1].x, chainPositions[i].y - chainPositions[i + 1].y);
+                stickDir = new Vector2(stickDir.x / stickDir.calcLen(), stickDir.y / stickDir.calcLen());
+                if (i != 0)
+                {
+                    chainPositions[i] = new Vector2(stickCentre.x + stickDir.x * ppl / 2, stickCentre.y + stickDir.y * ppl / 2);
+                }
+                chainPositions[i + 1] = new Vector2(stickCentre.x - stickDir.x * ppl / 2, stickCentre.y - stickDir.y * ppl / 2);
+            }
+            setTimeout(Update, 500/60);
+        }
+
+
+        function Draw()
+        {
+            ctx.beginPath();
+            ctx.moveTo(chainPositions[0].x + xPos, chainPositions[0].y + yPos);
+            for (i = 1; i < chainPositions.length; i++)
+            {
+                ctx.lineTo(chainPositions[i].x + xPos, chainPositions[i].y + yPos);
+            }
+            ctx.stroke();
+        }
+
+        function vectorAdd(v1, v2)
+        {
+            return new Vector2(v1.x + v2.x, v1.y + v2.y);
+        }
+
+        window.addEventListener('resize', function(event) {
+            c.width = window.innerWidth;
+            c.height = window.innerHeight;
+            ctx.translate(c.width / 2, c.height / 2);
+            ctx.scale(1.5, -1.5);
+        }, 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> 
\ No newline at end of file
