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Lissajous curves
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<iframe 
    src="https://jsxgraph.uni-bayreuth.de/share/iframe/lissajous-curves" 
    style="border: 1px solid black; overflow: hidden; width: 550px; aspect-ratio: 55 / 65;" 
    name="JSXGraph example: Lissajous curves" 
    allowfullscreen
></iframe>
This code has to 
<div id="board-0-wrapper" class="jxgbox-wrapper " style="width: 100%; ">
   <div id="board-0" class="jxgbox" style="aspect-ratio: 1 / 1; width: 100%;" data-ar="1 / 1"></div>
</div>

<script type = "text/javascript"> 
    /*
    This example is licensed under a 
    Creative Commons Attribution ShareAlike 4.0 International License.
    https://creativecommons.org/licenses/by-sa/4.0/
    
    Please note you have to mention 
    The Center of Mobile Learning with Digital Technology
    in the credits.
    */
    
    const BOARDID = 'board-0';

    var board = JXG.JSXGraph.initBoard(BOARDID, { axis: true, boundingbox: [-12, 10, 12, -10] });
    board.suspendUpdate();
    var a = board.create('slider', [[2, 8], [6, 8], [0, 3, 6]], { name: 'a' });
    var b = board.create('slider', [[2, 7], [6, 7], [0, 2, 6]], { name: 'b' });
    var A = board.create('slider', [[2, 6], [6, 6], [0, 3, 6]], { name: 'A' });
    var B = board.create('slider', [[2, 5], [6, 5], [0, 3, 6]], { name: 'B' });
    var delta = board.create('slider', [[2, 4], [6, 4], [0, 0, Math.PI]], { name: 'δ' });
    
    var c = board.create('curve', [
              function(t) { return A.Value() * Math.sin(a.Value() * t + delta.Value()); },
              function(t) { return B.Value() * Math.sin(b.Value() * t); },
              0, 2 * Math.PI], { strokeColor: '#aa2233', strokeWidth: 3 });
    board.unsuspendUpdate();
 </script> 
/*
This example is licensed under a 
Creative Commons Attribution ShareAlike 4.0 International License.
https://creativecommons.org/licenses/by-sa/4.0/

Please note you have to mention 
The Center of Mobile Learning with Digital Technology
in the credits.
*/

const BOARDID = 'your_div_id'; // Insert your id here!

var board = JXG.JSXGraph.initBoard(BOARDID, { axis: true, boundingbox: [-12, 10, 12, -10] });
board.suspendUpdate();
var a = board.create('slider', [[2, 8], [6, 8], [0, 3, 6]], { name: 'a' });
var b = board.create('slider', [[2, 7], [6, 7], [0, 2, 6]], { name: 'b' });
var A = board.create('slider', [[2, 6], [6, 6], [0, 3, 6]], { name: 'A' });
var B = board.create('slider', [[2, 5], [6, 5], [0, 3, 6]], { name: 'B' });
var delta = board.create('slider', [[2, 4], [6, 4], [0, 0, Math.PI]], { name: 'δ' });

var c = board.create('curve', [
          function(t) { return A.Value() * Math.sin(a.Value() * t + delta.Value()); },
          function(t) { return B.Value() * Math.sin(b.Value() * t); },
          0, 2 * Math.PI], { strokeColor: '#aa2233', strokeWidth: 3 });
board.unsuspendUpdate();
<jsxgraph width="100%" aspect-ratio="1 / 1" title="Lissajous curves" description="This construction was copied from JSXGraph examples database: BTW HERE SHOULD BE A GENERATED LINKuseGlobalJS="false">
   /*
   This example is licensed under a 
   Creative Commons Attribution ShareAlike 4.0 International License.
   https://creativecommons.org/licenses/by-sa/4.0/
   
   Please note you have to mention 
   The Center of Mobile Learning with Digital Technology
   in the credits.
   */
   
   var board = JXG.JSXGraph.initBoard(BOARDID, { axis: true, boundingbox: [-12, 10, 12, -10] });
   board.suspendUpdate();
   var a = board.create('slider', [[2, 8], [6, 8], [0, 3, 6]], { name: 'a' });
   var b = board.create('slider', [[2, 7], [6, 7], [0, 2, 6]], { name: 'b' });
   var A = board.create('slider', [[2, 6], [6, 6], [0, 3, 6]], { name: 'A' });
   var B = board.create('slider', [[2, 5], [6, 5], [0, 3, 6]], { name: 'B' });
   var delta = board.create('slider', [[2, 4], [6, 4], [0, 0, Math.PI]], { name: 'δ' });
   
   var c = board.create('curve', [
             function(t) { return A.Value() * Math.sin(a.Value() * t + delta.Value()); },
             function(t) { return B.Value() * Math.sin(b.Value() * t); },
             0, 2 * Math.PI], { strokeColor: '#aa2233', strokeWidth: 3 });
   board.unsuspendUpdate();
</jsxgraph>
Lissajous curve (Lissajous figure or Bowditch curve) is the graph of the system of parametric equations $$x=A\sin(at+\delta),\quad y=B\sin(bt).$$
// Define the id of your board in BOARDID

var board = JXG.JSXGraph.initBoard(BOARDID, { axis: true, boundingbox: [-12, 10, 12, -10] });
board.suspendUpdate();
var a = board.create('slider', [[2, 8], [6, 8], [0, 3, 6]], { name: 'a' });
var b = board.create('slider', [[2, 7], [6, 7], [0, 2, 6]], { name: 'b' });
var A = board.create('slider', [[2, 6], [6, 6], [0, 3, 6]], { name: 'A' });
var B = board.create('slider', [[2, 5], [6, 5], [0, 3, 6]], { name: 'B' });
var delta = board.create('slider', [[2, 4], [6, 4], [0, 0, Math.PI]], { name: 'δ' });

var c = board.create('curve', [
          function(t) { return A.Value() * Math.sin(a.Value() * t + delta.Value()); },
          function(t) { return B.Value() * Math.sin(b.Value() * t); },
          0, 2 * Math.PI], { strokeColor: '#aa2233', strokeWidth: 3 });
board.unsuspendUpdate();

license

This example is licensed under a Creative Commons Attribution ShareAlike 4.0 International License.
Please note you have to mention The Center of Mobile Learning with Digital Technology in the credits.