Applets:Periodendauer periodischer Signale: Difference between revisions

Revision as of 09:47, 18 September 2017

Funktion: $$x(t) = A_1\cdot cos\Big(2\pi f_1\cdot t- \frac{2\pi}{360}\cdot \phi_1\Big)+A_2\cdot cos\Big(2\pi f_2\cdot t- \frac{2\pi}{360}\cdot \phi_2\Big)$$

Gitterlinien zeigen

@@ Line 43: / Line 43: @@
 <div id="plotBoxHtml" class="jxgbox" style="width:600px; height:600px; border:1px solid black; margin:170px 20px 0px 0px;"></div>
 <div id="cnfBoxHtml" class="jxgbox" style="width:600px; height:150px; margin:-760px 20px 0px 0px;"></div>
-<div id="outBoxHtml" class="jxgbox" style="width:600px; height:100px; margin:625px 20px 0px 0px;"></div>
 <script type="text/javascript">
 function drawNow() {
-//Grundeinstellungen der beiden Applets
+    // Grundeinstellungen der beiden Applets
-JXG.Options.text.useMathJax = true;
+    JXG.Options.text.useMathJax = true;
-plotBox = JXG.JSXGraph.initBoard('plotBoxHtml', {showCopyright:false, axis:false, zoom:{factorX:1.1, factorY:1.1, wheel:true, needshift:true, eps: 0.1}, grid:false, boundingbox: [-0.5, 2.2, 12.4, -2.2]});
+    cnfBox = JXG.JSXGraph.initBoard('cnfBoxHtml', {
-cnfBox = JXG.JSXGraph.initBoard('cnfBoxHtml', {showCopyright:false, showNavigation:false, axis:false, grid:false, zoom:{enabled:false}, pan:{enabled:false}, boundingbox: [-1, 2.2, 12.4, -2.2]});
+        showCopyright: false, showNavigation: false, axis: false,
-var outBox = JXG.JSXGraph.initBoard('outBoxHtml', {showCopyright:false, showNavigation:false, axis:false, grid:false, zoom:{enabled:false}, pan:{enabled:false}, boundingbox: [-1, 2.2, 12.4, -2.2]});
+        grid: false, zoom: { enabled: false }, pan: { enabled: false },
-cnfBox.addChild(plotBox);
+        boundingbox: [-1, 2.2, 12.4, -2.2]
-cnfBox.addChild(outBox);
+    });
+    pltBox = JXG.JSXGraph.initBoard('pltBoxHtml', {
-//Einstellungen der Achsen
+        showCopyright: false, axis: false,
-xaxis = plotBox.create('axis', [[0, 0], [1,0]], {name:'\\[t/T\\]', withLabel:true, label:{position:'rt', offset:[-25, 15]}});
+        zoom: { factorX: 1.1, factorY: 1.1, wheel: true, needshift: true, eps: 0.1 },
-yaxis = plotBox.create('axis', [[0, 0], [0, 1]], {name:'\\[x(t)\\]', withLabel:true, label:{position:'rt', offset:[10, -5]}});
+        grid: false, boundingbox: [-0.5, 2.2, 12.4, -2.2]
+    });
+    cnfBox.addChild(pltBox);
-//Festlegen der Schieberegler
+    // Einstellungen der Achsen
-a = cnfBox.create('slider',[[-0.7,1.5],[3,1.5],[0,0.5,1]], {withLabel:false, withTicks:false, snapWidth:0.01}),
+    xaxis = pltBox.create('axis', [[0, 0], [1, 0]], {
-b = cnfBox.create('slider',[[-0.7,0.5],[3,0.5],[0,1,10]], {withLabel:false, withTicks:false, snapWidth:0.1}),
+        name: '$\\dfrac{t}{T}$',
-c = cnfBox.create('slider',[[-0.7,-0.5],[3,-0.5],[-180,0,180]], {withLabel:false, withTicks:false, snapWidth:5}),
+        withLabel: true, label: { position: 'rt', offset: [-25, -10] }
-d = cnfBox.create('slider',[[6,1.5],[9.7,1.5],[0,0.5,1]], {withLabel:false, withTicks:false, snapWidth:0.01}),
+    });
-e = cnfBox.create('slider',[[6,0.5],[9.7,0.5],[0,2,10]], {withLabel:false, withTicks:false, snapWidth:0.1}),
+    yaxis = pltBox.create('axis', [[0, 0], [0, 1]], {
-g = cnfBox.create('slider',[[6,-0.5],[9.7,-0.5],[-180,90,180]], {withLabel:false, withTicks:false, snapWidth:5}),
+        name: '$x(t)$',
-t = cnfBox.create('slider',[[-0.7,-1.5],[3,-1.5],[0,0,10]], {withLabel:false, withTicks:false, snapWidth:0.2}),
+        withLabel: true, label: { position: 'rt', offset: [10, -5] }
+    });
-//Definition der Ausgabefelder
+    // Erstellen der Schieberegler
-texta=cnfBox.create('text',[2.8,1.87, function()
+    sldA1 = cnfBox.create('slider', [ [-0.7, 1.5], [3, 1.5], [0, 0.5, 1] ], {
-  { return '\\[A_1= '+ Math.round(a.Value()*100)/100 +' \\text{ V}\\]';}], {fixed:true, visible:true, fontSize:14});
+        suffixlabel: '$A_1=$',
-textb=cnfBox.create('text',[2.8,0.87, function()
+        unitLabel: 'V', snapWidth: 0.01
-  { return '\\[f_1= '+ Math.round(b.Value()*100)/100 +' \\text{ kHz}\\]';}], {fixed:true, visible:true, fontSize:14});
+        }),
-textc=cnfBox.create('text',[2.8,-0.13, function()
+    sldF1 = cnfBox.create('slider', [ [-0.7, 0.5], [3, 0.5], [0, 1, 10] ], {
-  { return '\\[\\phi_1= '+ Math.round(c.Value()*100)/100 +' \\text{ Grad}\\]';}], {fixed:true, visible:true, fontSize:14});
+        suffixlabel: '$f_1=$',
-textd=cnfBox.create('text',[9.5,1.67, function()
+        unitLabel: 'kHz', snapWidth: 0.1
-  { return '\\[A_2= '+ Math.round(d.Value()*100)/100 +' \\text{ V}\\]';}], {fixed:true, visible:true, fontSize:14});
+    }),
-texte=cnfBox.create('text',[9.5,0.67, function()
+    sldPHI1 = cnfBox.create('slider', [ [-0.7, -0.5], [3, -0.5], [-180, 0, 180] ], {
-  { return '\\[f_2= '+ Math.round(e.Value()*100)/100 +' \\text{ kHz}\\]';}], {fixed:true, visible:true, fontSize:14});
+        suffixlabel: '$\\phi_1=$',
-textg=cnfBox.create('text',[9.5,-0.33, function()
+        unitLabel: 'Grad', snapWidth: 5
-  { return '\\[\\phi_2= '+ Math.round(g.Value()*100)/100 +' \\text{ Grad}\\]';}], {fixed:true, visible:true, fontSize:14});
+    }),
-textt=cnfBox.create('text',[2.8,-1.2, function()
+    sldA2 = cnfBox.create('slider', [ [6, 1.5], [9.7, 1.5], [0, 0.5, 1] ], {
-  { return '\\[t= '+ Math.round(t.Value()*100)/100 +' \\]';}], {fixed:true, visible:true, fontSize:14});
+        suffixlabel: '$A_2=$',
+        unitLabel: 'V', snapWidth: 0.01
+    }),
+    sldF2 = cnfBox.create('slider', [ [6, 0.5], [9.7, 0.5], [0, 2, 10] ], {
+        suffixlabel: '$f_2=$',
+        unitLabel: 'kHz', snapWidth: 0.1
+    }),
+    sldPHI2 = cnfBox.create('slider', [ [6, -0.5], [9.7, -0.5], [-180, 90, 180] ], {
+        suffixlabel: '$\\phi_2=$',
+        unitLabel: 'Grad', snapWidth: 5
+    }),
+    sldT = cnfBox.create('slider', [ [-0.7, -1.5], [3, -1.5], [0, 0, 10] ], {
+        suffixlabel: '$t=$',
+        unitLabel: 's', snapWidth: 0.2
+    }),
-textergebnis1=outBox.create('text',[-1,1.5, function()
+    // Definition der Funktion
-  { return '\\[x(t)= '+ Math.round((a.Value()*Math.cos(2*Math.PI*b.Value()*t.Value()-2*Math.PI*c.Value()/360)+d.Value()*Math.cos(2*Math.PI*e.Value()*t.Value()-2*Math.PI*g.Value()/360))*1000)/1000 +' \\]';}], {fixed:true, visible:true, fontSize:14});
+    signaldarstellung = pltBox.create('functiongraph', [function(x) {
-textergebnis2=outBox.create('text',[1.5,1.5, function()
+        return (sldA1.Value() * Math.cos(2 * Math.PI * sldF1.Value() * x - 2 * Math.PI * sldPHI1.Value() / 360) + sldA2.Value() * Math.cos(2 * Math.PI * sldF2.Value() * x - 2 * Math.PI * sldPHI2.Value() / 360))
-  { return '\\[x(t+T_0)= '+ Math.round((a.Value()*Math.cos(2*Math.PI*b.Value()*(t.Value()+Math.round(getT0() *1000)/1000)-c.Value())+d.Value()*Math.cos(2*Math.PI*e.Value()*(t.Value()+Math.round(getT0() *1000)/1000)-g.Value()))*1000)/1000 +' \\]';}], {fixed:true, visible:true, fontSize:14});
+    }], {
-textergebnis3=outBox.create('text',[5,1.5, function()
+        strokeColor: "red"
-  { return '\\[x(t+2T_0)= '+ Math.round((a.Value()*Math.cos(2*Math.PI*b.Value()*(t.Value()+2*Math.round(getT0() *1000)/1000)-c.Value())+d.Value()*Math.cos(2*Math.PI*e.Value()*(t.Value()+2*Math.round(getT0() *1000)/1000)-g.Value()))*1000)/1000 +' \\]';}], {fixed:true, visible:true, fontSize:14});
+    });
-textergebnis4=outBox.create('text',[8.5,1.5, function()
-{var x = new Array(50000);
-for (var i = 0; i < 50001; i++) {x[i] = Math.round((a.Value()*Math.cos(2*Math.PI*b.Value()*(i/1000)-2*Math.PI*c.Value()/360)+d.Value()*Math.cos(2*Math.PI*e.Value()*(i/1000)-2*Math.PI*g.Value()/360)) *1000)/1000;};
-return '\\[x_{max}= '+ Math.max.apply(Math,x)+' \\]';}], {fixed:true, visible:true, fontSize:14});
-textergebnis5=outBox.create('text',[10.8,1.5, function()
-  { return '\\[T_0= '+ Math.round(getT0() *100)/100 +' \\]';}], {fixed:true, visible:true, strokeColor:'blue', fontSize:14});
-//Definition der Funktion
+    // Definition des Punktes p_T0, des Hilfspunktes p_T0h und der Geraden l_T0 für Periodendauer T_0
-signaldarstellung = plotBox.create('functiongraph',[function(x){
+    p_T0 = pltBox.create('point', [
-         return (a.Value()*Math.cos(2*Math.PI*b.Value()*x-2*Math.PI*c.Value()/360)+d.Value()*Math.cos(2*Math.PI*e.Value()*x-2*Math.PI*g.Value()/360))
+        function() {
-     }], {strokeColor: "red"});
+            return (Math.round(getT0() * 100) / 100);
+        },
+         function() {
+            return sldA1.Value() * Math.cos(2 * Math.PI * sldF1.Value() * (Math.round(getT0() * 100) / 100) - 2 * Math.PI * sldPHI1.Value() / 360) +
+                sldA2.Value() * Math.cos(2 * Math.PI * sldF2.Value() * (Math.round(getT0() * 100) / 100) - 2 * Math.PI * sldPHI2.Value() / 360);
+        }],
+        { color: "blue", fixed: true, label: false, size: 1, name: '' }
+    );
+     p_T0h = pltBox.create('point',
+        [function() { return (Math.round(getT0() * 100) / 100); }, 2],
+        { visible: false, color: "blue", fixed: true, label: false, size: 1, name: '' }
+    );
+    l_T0 = pltBox.create('line', [p_T0, p_T0h])
-//Definition des Punktes p_T0, des Hilfspunktes p_T0h und der Geraden l_T0 für Periodendauer T_0
+    // Bestimmung des Wertes T_0 mit der Funktion von Siebenwirth
-p_T0=plotBox.create('point', [function(){ return Math.round(getT0() *100)/100;},
+    setInterval(function() {
-      function(){ return a.Value()*Math.cos(2*Math.PI*b.Value()*(Math.round(getT0() *100)/100)-2*Math.PI*c.Value()/360)
+         document.getElementById("T_0").innerHTML = Math.round(getT0() * 100) / 100;
-         +d.Value()*Math.cos(2*Math.PI*e.Value()*(Math.round(getT0() *100)/100)-2*Math.PI*g.Value()/360);}], {color:"blue", fixed:true, label:false, size:1, name:''})
+    }, 50);
-p_T0h = plotBox.create('point', [function(){ return Math.round(getT0() *100)/100;}, 2], {visible: false, color:"blue", fixed:true, label:false, size:1, name:''})
-l_T0 = plotBox.create('line', [p_T0, p_T0h])
 };