diff --git a/4-12.html b/4-12.html
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+++ b/4-12.html
@@ -0,0 +1,238 @@
+<!--
+    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 4-12
+        </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>
+        <div class="dropdown">
+            <button class="dropbtn" id="btn">2 Masses</button>
+            <div class="dropdown-content">
+                <button onclick="num(2)">2 Masses</button>
+                <button onclick="num(3)">3 Masses</button>
+                <button onclick="num(4)">4 Masses</button>
+                <button onclick="num(5)">5 Masses</button>
+                <button onclick="num(6)">6 Masses</button>
+                <button onclick="num(7)">7 Masses</button>
+                <button onclick="num(8)">8 Masses</button>
+            </div>
+        </div>  
+        <div class="dropdown" id="m">
+            <button class="dropbtnm" id="btnm">Mode 1</button>   
+            <div class="dropdown-content">
+                <button onclick="mum(1)" id="btn1">Mode 1</button>
+                <button onclick="mum(2)" id="btn2">Mode 2</button>
+                <button onclick="mum(3)" id="btn3">Mode 3</button>
+                <button onclick="mum(4)" id="btn4">Mode 4</button>
+                <button onclick="mum(5)" id="btn5">Mode 5</button>
+                <button onclick="mum(6)" id="btn6">Mode 6</button>
+                <button onclick="mum(7)" id="btn7">Mode 7</button>
+                <button onclick="mum(8)" id="btn8">Mode 8</button>
+            </div>
+        </div>
+        
+        <script>
+        var c = document.getElementById("myCanvas");
+        var ctx = c.getContext("2d");
+        ctx.canvas.width = window.innerWidth;
+        ctx.canvas.height = window.innerHeight;
+    
+        var w = 1;
+        var amp = 0.8 / n;
+        var n = 2;
+        var m = 1;
+        var t = 0;
+        var dt = 0.1;
+        var xPos = 0;
+        var yPos = 0;
+
+        function num(nn)
+        {
+            n = nn;
+            document.getElementById("btn").textContent = n.toString() + " Masses";
+            if (m > n)
+            {
+                m = n;
+                document.getElementById("btnm").textContent = "Mode " + m.toString();
+            }
+        }
+
+        function mum(mm)
+        {
+            m = mm;
+            document.getElementById("btnm").textContent = "Mode " + m.toString();
+
+        }
+
+        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;
+            amp = 0.8 / n;
+            for (i = 1; i <= n; i++)
+            {
+                document.getElementById("btn" + i.toString()).style.visibility = "visible";
+            }
+            for (i = n + 1; i <= 8; i++)
+            {
+                document.getElementById("btn" + i.toString()).style.visibility = "hidden";
+            }
+            setTimeout(Update, 1000/60)
+        }
+
+        function Draw()
+        {
+            ctx.beginPath();
+            ctx.arc(xPos, yPos, 100, 0, Math.PI * 2);
+            ctx.stroke();
+            for (i = 0; i < n; i++)
+            {
+                if (2 * w * Math.sin(Math.PI * m / n) > 0.0001)
+                {
+                    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
+                {
+                    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);
+                }
+            }
+        }
+
+        function connectTwoTheta(theta1, theta2)
+        {
+            if (theta1 > theta2)
+            {
+                theta2 += Math.PI * 2;
+            }
+            drawSpring(1, 3, Math.abs(theta1 - theta2), -10, Math.ceil(50 / n), theta1, 105, 0.1, xPos, yPos);
+        }
+
+        function drawSpring(a, b, tSize, rSize, numLoops, t, r, pStep, x, y)
+        {
+            var pStart = 0;
+            var pEnd = (3 * Math.PI / 2) + (2 * Math.PI * numLoops);
+            var tEnd = a * pEnd - b * Math.sin(pEnd);
+            var rEnd = a + b;
+            var tFactor = tSize / tEnd;
+            var rFactor = rSize / rEnd;
+            var tShift = t /*- a * (Math.PI / 2) + b * Math.sin(Math.PI / 2) - Math.PI/ 2*/;
+            var rShift = r - a + b * Math.cos(Math.PI / 2);
+            for (p = pStart; p <= pEnd; p += pStep)
+            {
+                var theta = tShift + tFactor * (a * p - b * Math.sin(p));
+                var radius = rShift + rFactor * (a - b * Math.cos(p));
+                ctx.beginPath();
+                ctx.moveTo(x + radius * Math.cos(theta), y + radius * Math.sin(theta));
+                theta = tShift + tFactor * (a * (p + pStep) - b * Math.sin((p + pStep)));
+                radius = rShift + rFactor * (a - b * Math.cos(p + pStep));
+                ctx.lineTo(x + radius * Math.cos(theta), y + radius * Math.sin(theta));
+                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
