Applets:Periodendauer periodischer Signale: Difference between revisions

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<script type="text/javascript">
<script type="text/javascript">
function drawNow() {
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,
cnfBox.addChild(plotBox);
        grid: false, zoom: { enabled: false }, pan: { enabled: false },
        boundingbox: [-1, 2.2, 12.4, -2.2]
    });
    pltBox = JXG.JSXGraph.initBoard('pltBoxHtml', {
        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.addChild(pltBox);


    // Einstellungen der Achsen
    xaxis = pltBox.create('axis', [[0, 0], [1, 0]], {
        name: '$\\dfrac{t}{T}$',
        withLabel: true, label: { position: 'rt', offset: [-25, -10] }
    });
    yaxis = pltBox.create('axis', [[0, 0], [0, 1]], {
        name: '$x(t)$',
        withLabel: true, label: { position: 'rt', offset: [10, -5] }
    });


//Einstellungen der Achsen
    // Erstellen der Schieberegler
xaxis = plotBox.create('axis', [[0, 0], [1,0]], {name:'\\[t/T\\]', withLabel:true, label:{position:'rt', offset:[-25, 15]}});
    sldA1 = cnfBox.create('slider', [ [-0.7, 1.5], [3, 1.5], [0, 0.5, 1] ], {
yaxis = plotBox.create('axis', [[0, 0], [0, 1]], {name:'\\[x(t)\\]', withLabel:true, label:{position:'rt', offset:[10, -5]}});
        suffixlabel: '$A_1=$',
        unitLabel: 'V', snapWidth: 0.01
        }),
    sldF1 = cnfBox.create('slider', [ [-0.7, 0.5], [3, 0.5], [0, 1, 10] ], {
        suffixlabel: '$f_1=$',
        unitLabel: 'kHz', snapWidth: 0.1
    }),
    sldPHI1 = cnfBox.create('slider', [ [-0.7, -0.5], [3, -0.5], [-180, 0, 180] ], {
        suffixlabel: '$\\phi_1=$',
        unitLabel: 'Grad', snapWidth: 5
    }),
    sldA2 = cnfBox.create('slider', [ [6, 1.5], [9.7, 1.5], [0, 0.5, 1] ], {
        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
    }),


//Festlegen der Schieberegler
a = cnfBox.create('slider',[[-0.7,1.5],[3,1.5],[0,0.5,1]], {withLabel:false, withTicks:false, snapWidth:0.01}),
b = cnfBox.create('slider',[[-0.7,0.5],[3,0.5],[0,1,10]], {withLabel:false, withTicks:false, snapWidth:0.1}),
c = cnfBox.create('slider',[[-0.7,-0.5],[3,-0.5],[-180,0,180]], {withLabel:false, withTicks:false, snapWidth:5}),
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}),
g = cnfBox.create('slider',[[6,-0.5],[9.7,-0.5],[-180,90,180]], {withLabel:false, withTicks:false, snapWidth:5}),
t = cnfBox.create('slider',[[-0.7,-1.5],[3,-1.5],[0,0,10]], {withLabel:false, withTicks:false, snapWidth:0.2}),


//Definition der Funktion
//Definition der Funktion
signaldarstellung = plotBox.create('functiongraph',[function(x){
signaldarstellung = plotBox.create('functiongraph',[function(x){
         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))
         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))
     }], {strokeColor: "red"});
     }], {strokeColor: "red"});


//Definition des Punktes p_T0, des Hilfspunktes p_T0h und der Geraden l_T0 für Periodendauer T_0
//Definition des Punktes p_T0, des Hilfspunktes p_T0h und der Geraden l_T0 für Periodendauer T_0
p_T0=plotBox.create('point', [function(){ return Math.round(getT0() *100)/100;},
p_T0=plotBox.create('point', [function(){ return Math.round(getT0() *100)/100;},
       function(){ return a.Value()*Math.cos(2*Math.PI*b.Value()*(Math.round(getT0() *100)/100)-2*Math.PI*c.Value()/360)
       function(){ return sldA1.Value()*Math.cos(2*Math.PI*sldF1.Value()*(Math.round(getT0() *100)/100)-2*Math.PI*sldPHI1.Value()/360)
         +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:''})
         +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 = plotBox.create('point', [function(){ return Math.round(getT0() *100)/100;}, 2], {visible: false, color:"blue", fixed:true, label:false, size:1, name:''})
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])
l_T0 = plotBox.create('line', [p_T0, p_T0h])
    // Definition der Funktion
    signaldarstellung = pltBox.create('functiongraph', [function(x) {
        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))
    }], {
        strokeColor: "red"
    });
    // Definition des Punktes p_T0, des Hilfspunktes p_T0h und der Geraden l_T0 für Periodendauer T_0
    p_T0 = pltBox.create('point', [
        function() {
            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])
   


};
};
Line 84: Line 150:


         var A, B, C, Q;
         var A, B, C, Q;
         if (b.Value() < e.Value()) {
         if (sldF1.Value() < sldF2.Value()) {
             A = b.Value();
             A = sldF1.Value();
             B = e.Value();
             B = sldF2.Value();
         } else {
         } else {
             B = b.Value();
             B = sldF1.Value();
             A = e.Value();
             A = sldF2.Value();
         }
         }


Revision as of 10:02, 18 September 2017

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

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