diff --git a/4-12.html b/4-12.html
index d1f45c6..a24136a 100644
--- a/4-12.html
+++ b/4-12.html
@@ -164,28 +164,61 @@
             ctx.beginPath();
             ctx.arc(xPos, yPos, 100, 0, Math.PI * 2);
             ctx.stroke();
-            for (i = 0; i < n; i++)
+            if (m % 2 == 0)
             {
-                if (2 * w * Math.sin(Math.PI * m / n) > 0.0001)
+                mn = Math.floor(m / 2);
+                console.log("cos" + mn.toString());
+                for (i = 0; i < n; i++)
                 {
-                    var theta = Math.PI * 2 * i / n;
-                    theta += Math.cos(i * 2 * Math.PI * m / n) * amp * Math.cos(2 * w * Math.sin(Math.PI * m / n) * t);
-                    var theta2 = Math.PI * 2 * (i + 1) / n;
-                    theta2 += Math.cos((i+1) * 2 * Math.PI * m / n) * amp * Math.cos(2 * w * Math.sin(Math.PI * m / n) * t);
-                    ctx.beginPath();
-                    ctx.arc(xPos + 100 * Math.cos(theta), yPos + 100 * Math.sin(theta), 10, 0, Math.PI * 2);
-                    ctx.fill();
-                    connectTwoTheta(theta, theta2);
-                } else
+                    if (2 * w * Math.sin(Math.PI * mn / n) > 0.0001)
+                    {
+                        var theta = Math.PI * 2 * i / n;
+                        theta += Math.cos(i * 2 * Math.PI * mn / n) * amp * Math.cos(2 * w * Math.sin(Math.PI * mn / n) * t);
+                        var theta2 = Math.PI * 2 * (i + 1) / n;
+                        theta2 += Math.cos((i+1) * 2 * Math.PI * mn / n) * amp * Math.cos(2 * w * Math.sin(Math.PI * mn / n) * t);
+                        ctx.beginPath();
+                        ctx.arc(xPos + 100 * Math.cos(theta), yPos + 100 * Math.sin(theta), 10, 0, Math.PI * 2);
+                        ctx.fill();
+                        connectTwoTheta(theta, theta2);
+                    } else
+                    {
+                        var theta = Math.PI * 2 * i / n;
+                        theta += Math.cos(i * 2 * Math.PI * mn / n) * amp * w * t;
+                        var theta2 = Math.PI * 2 * (i + 1) / n;
+                        theta2 += Math.cos((i+1) * 2 * Math.PI * mn / n) * amp * w * t;
+                        ctx.beginPath();
+                        ctx.arc(xPos + 100 * Math.cos(theta), yPos + 100 * Math.sin(theta), 10, 0, Math.PI * 2);
+                        ctx.fill();
+                        connectTwoTheta(theta, theta2);
+                    }
+                }
+            } else
+            {
+                mn = Math.floor(m / 2);
+                console.log("sin" + mn.toString());
+                for (i = 0; i < n; i++)
                 {
-                    var theta = Math.PI * 2 * i / n;
-                    theta += Math.cos(i * 2 * Math.PI * m / n) * amp * w * t;
-                    var theta2 = Math.PI * 2 * (i + 1) / n;
-                    theta2 += Math.cos((i+1) * 2 * Math.PI * m / n) * amp * w * t;
-                    ctx.beginPath();
-                    ctx.arc(xPos + 100 * Math.cos(theta), yPos + 100 * Math.sin(theta), 10, 0, Math.PI * 2);
-                    ctx.fill();
-                    connectTwoTheta(theta, theta2);
+                    if (2 * w * Math.sin(Math.PI * mn / n) > 0.0001)
+                    {
+                        var theta = Math.PI * 2 * i / n;
+                        theta += Math.sin(i * 2 * Math.PI * mn / n) * amp * Math.cos(2 * w * Math.sin(Math.PI * mn / n) * t);
+                        var theta2 = Math.PI * 2 * (i + 1) / n;
+                        theta2 += Math.sin((i+1) * 2 * Math.PI * mn / n) * amp * Math.cos(2 * w * Math.sin(Math.PI * mn / n) * t);
+                        ctx.beginPath();
+                        ctx.arc(xPos + 100 * Math.cos(theta), yPos + 100 * Math.sin(theta), 10, 0, Math.PI * 2);
+                        ctx.fill();
+                        connectTwoTheta(theta, theta2);
+                    } else
+                    {
+                        var theta = Math.PI * 2 * i / n;
+                        theta += Math.cos(i * 2 * Math.PI * mn / n) * amp * w * t;
+                        var theta2 = Math.PI * 2 * (i + 1) / n;
+                        theta2 += Math.cos((i+1) * 2 * Math.PI * mn / n) * amp * w * t;
+                        ctx.beginPath();
+                        ctx.arc(xPos + 100 * Math.cos(theta), yPos + 100 * Math.sin(theta), 10, 0, Math.PI * 2);
+                        ctx.fill();
+                        connectTwoTheta(theta, theta2);
+                    }
                 }
             }
         }
diff --git a/5-15.html b/5-15.html
new file mode 100644
index 0000000..ddcd2a9
--- /dev/null
+++ b/5-15.html
@@ -0,0 +1,170 @@
+<!--
+    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 5-15
+        </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 m = 250;
+        var s = 1;
+        var u = 10;
+        var t = 0;
+        var w = 160;
+        var h = 100;
+        var x = 0;
+        var sdt = 3;
+        var st = 3;
+        var sr = 5;
+        var six = -100;
+        var snowballPositions = new Array();
+        var snowballDirections = new Array();
+        var dt = 0.1;
+        var xPos = 0;
+        var yPos = 0;
+
+        ctx.translate(ctx.canvas.width / 2, ctx.canvas.height / 2);
+        ctx.scale(1.5, 1.5);
+
+
+        function Clear(ctx)
+        {
+            ctx.clearRect(-c.width, -c.height, c.width * 2, c.height * 2);
+        }
+
+        function Update()
+        {
+            Clear(ctx);
+            Draw();
+            t += dt;
+            st += dt;
+            x = calcX(t);
+            setTimeout(Update, 1000/60)
+        }
+
+        function calcX(gt)
+        {
+            return u * gt - m * u * Math.log(1 + 2 * s * gt / m) / (2 * s);
+        }
+
+        function Draw()
+        {
+            ctx.beginPath();
+            ctx.rect(xPos + x - w / 2, yPos - h / 2, w, h);
+            ctx.stroke();
+            ctx.beginPath();
+            ctx.arc(xPos + x - w / 4 - h/8, yPos + h / 2 + h / 8, h/8, 0, Math.PI * 2);
+            ctx.stroke();
+            ctx.beginPath();
+            ctx.arc(xPos + x + w / 4 + h/8, yPos + h / 2 + h / 8, h/8, 0, Math.PI * 2);
+            ctx.stroke();
+            if (st > sdt)
+            {
+                st -= sdt;
+                snowballPositions.push(six);
+                snowballDirections.push(1);
+            }
+            for (i = 0; i < snowballPositions.length; i++)
+            {
+                if (snowballPositions[i] < x - w/2 - sr || snowballDirections[i] == -1)
+                {
+                    snowballPositions[i] += u * dt * snowballDirections[i];
+                } else
+                {
+                    snowballDirections[i] = -1;
+                }
+                ctx.beginPath();
+                ctx.arc(xPos + snowballPositions[i], yPos - h/4, sr, 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);
+        }, 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/5-16.html b/5-16.html
new file mode 100644
index 0000000..149b4c9
--- /dev/null
+++ b/5-16.html
@@ -0,0 +1,174 @@
+<!--
+    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 5-16
+        </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 m = 250;
+        var s = 1;
+        var u = 10;
+        var t = 0;
+        var w = 160;
+        var h = 100;
+        var x = 0;
+        var sdt = 3;
+        var st = 3;
+        var sr = 5;
+        var six = -100;
+        var snowballPositions = new Array();
+        var snowballDirections = new Array();
+        var dt = 0.1;
+        var xPos = 0;
+        var yPos = 0;
+
+        ctx.translate(ctx.canvas.width / 2, ctx.canvas.height / 2);
+        ctx.scale(1.5, 1.5);
+
+
+        function Clear(ctx)
+        {
+            ctx.clearRect(-c.width, -c.height, c.width * 2, c.height * 2);
+        }
+
+        function Update()
+        {
+            Clear(ctx);
+            Draw();
+            t += dt;
+            st += dt;
+            x = calcX(t);
+            setTimeout(Update, 1000/60)
+        }
+
+        function calcX(gt)
+        {
+            return u * gt - m * u * Math.log(1 + 2 * s * gt / m) / (2 * s);
+        }
+
+        function Draw()
+        {
+            ctx.beginPath();
+            ctx.rect(xPos + x - w / 2, yPos - h / 2, w, h);
+            ctx.stroke();
+            ctx.beginPath();
+            ctx.arc(xPos + x - w / 4 - h/8, yPos + h / 2 + h / 8, h/8, 0, Math.PI * 2);
+            ctx.stroke();
+            ctx.beginPath();
+            ctx.arc(xPos + x + w / 4 + h/8, yPos + h / 2 + h / 8, h/8, 0, Math.PI * 2);
+            ctx.stroke();
+            if (st > sdt)
+            {
+                st -= sdt;
+                snowballPositions.push(six);
+                snowballDirections.push(1);
+            }
+            for (i = 0; i < snowballPositions.length; i++)
+            {
+                y = -h/4;
+                if (snowballPositions[i] < x - w/2 - sr)
+                {
+                    snowballPositions[i] += u * dt * snowballDirections[i];
+                } else
+                {
+                    snowballDirections[i] = 0;
+                    nr = Math.floor(w / (2 * sr));
+                    snowballPositions[i] = x - w/2 + sr + 2 * sr * (i % nr);
+                    y = h/2 - sr - 2 * sr * Math.floor(i / nr);
+                }
+                ctx.beginPath();
+                ctx.arc(xPos + snowballPositions[i], yPos + y, sr, 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);
+        }, 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