Difference between revisions of "Applets:Periodendauer periodischer Signale"
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<html> | <html> | ||
<head> | <head> | ||
− | + | <script type="text/javascript" src="http://cdnjs.cloudflare.com/ajax/libs/jsxgraph/0.99.6/jsxgraphcore.js"></script> | |
− | + | <script type="text/javascript" src="https://cdn.rawgit.com/mathjax/MathJax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script> | |
− | + | <style> | |
− | + | .button1{ | |
− | <style> | + | background-color: black; |
− | + | border: none; | |
− | + | color: white; | |
− | + | font-family: arial; | |
− | + | padding: 8px 20px; | |
− | + | text-align: center; | |
− | + | text-decoration: none; | |
− | + | display: inline-block; | |
− | + | font-size: 16px; | |
− | + | border-radius: 15px; | |
− | + | position:relative; | |
− | + | top: 205px; | |
− | + | left: 530px; | |
− | + | } | |
− | + | ||
− | } | + | .button1:active { |
+ | background-color: #939393;} | ||
+ | |||
+ | .formel { | ||
+ | background-color: #f5f5f5; | ||
+ | border-radius: 4px ; | ||
+ | padding: 20px 30px; | ||
+ | font-family: arial; | ||
+ | position:absolute; | ||
+ | top: 250px; | ||
+ | left: 10px; | ||
+ | } | ||
+ | |||
</style> | </style> | ||
</head> | </head> | ||
+ | <body> | ||
+ | |||
+ | <form id="myForm"> | ||
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<!-- Resetbutton, Checkbox und Formel --> | <!-- Resetbutton, Checkbox und Formel --> | ||
+ | <button class="button1" style="font-size:0.750em" onclick="zurueck()">Reset</button> | ||
+ | <p><span class="separate" style="position:absolute; top:180px; left:550px; font-family:arial; font-size:0.750em;">mit Gitter<input name="gridbox" id="gridbox" type="checkbox" onclick="showgrid();" checked="checked"></span></p> | ||
+ | <box class="formel">\(x(t)=A_1\cdot cos\Big(2\pi f_1\cdot t- \frac{2\pi}{360}\cdot \phi_1\Big)+A_2\cdot cos\Big(2\pi f_2\cdot t- \frac{2\pi}{360}\cdot \phi_2\Big)\)</box> | ||
+ | |||
+ | <div id="box1" class="jxgbox" style="width:600px; height:600px; border:1px solid black; margin:300px 20px 100px 0px;"></div> | ||
+ | <div id="box2" class="jxgbox" style="width:500px; height:200px; border:1px solid white; margin:-1000px 20px 100px 0px;"></div> | ||
+ | <div id="box3" class="jxgbox" style="width:600px; height:100px; border:1px solid white; margin:700px 20px 100px 0px;"></div> | ||
+ | |||
+ | <script type="text/javascript"> | ||
+ | |||
+ | //Grundeinstellungen der beiden Applets | ||
+ | JXG.Options.text.useMathJax = true; | ||
+ | var brd1 = JXG.JSXGraph.initBoard('box1', {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]}); | ||
+ | var brd2 = JXG.JSXGraph.initBoard('box2', {showCopyright:false, showNavigation:false, axis:false, grid:false, zoom:{enabled:false}, pan:{enabled:false}, boundingbox: [-1, 2.2, 12.4, -2.2]}); | ||
+ | var brd3 = JXG.JSXGraph.initBoard('box3', {showCopyright:false, showNavigation:false, axis:false, grid:false, zoom:{enabled:false}, pan:{enabled:false}, boundingbox: [-1, 2.2, 12.4, -2.2]}); | ||
+ | brd2.addChild(brd1); | ||
+ | brd2.addChild(brd3); | ||
+ | |||
+ | //Einstellungen der Achsen | ||
+ | xaxis = brd1.create('axis', [[0, 0], [1,0]], {name:'\\[t/T\\]', withLabel:true, label:{position:'rt', offset:[-25, 15]}}); | ||
+ | yaxis = brd1.create('axis', [[0, 0], [0, 1]], {name:'\\[x(t)\\]', withLabel:true, label:{position:'rt', offset:[10, -5]}}); | ||
+ | |||
+ | //Festlegen der Schieberegler | ||
+ | a = brd2.create('slider',[[-0.7,1.5],[3,1.5],[0,0.5,1]], {withLabel:false, withTicks:false, snapWidth:0.01}), | ||
+ | b = brd2.create('slider',[[-0.7,0.5],[3,0.5],[0,1,10]], {withLabel:false, withTicks:false, snapWidth:0.1}), | ||
+ | c = brd2.create('slider',[[-0.7,-0.5],[3,-0.5],[-180,0,180]], {withLabel:false, withTicks:false, snapWidth:5}), | ||
+ | d = brd2.create('slider',[[6,1.5],[9.7,1.5],[0,0.5,1]], {withLabel:false, withTicks:false, snapWidth:0.01}), | ||
+ | e = brd2.create('slider',[[6,0.5],[9.7,0.5],[0,2,10]], {withLabel:false, withTicks:false, snapWidth:0.1}), | ||
+ | g = brd2.create('slider',[[6,-0.5],[9.7,-0.5],[-180,90,180]], {withLabel:false, withTicks:false, snapWidth:5}), | ||
+ | t = brd2.create('slider',[[-0.7,-1.5],[3,-1.5],[0,0,10]], {withLabel:false, withTicks:false, snapWidth:0.2}), | ||
− | |||
− | |||
+ | //Definition der Ausgabefelder | ||
+ | texta=brd2.create('text',[3.2,1.7, function() | ||
+ | { return '\\[A_1= '+ Math.round(a.Value()*100)/100 +' \\text{ V}\\]';}], {fixed:true, visible:true}); | ||
+ | textb=brd2.create('text',[3.2,0.7, function() | ||
+ | { return '\\[f_1= '+ Math.round(b.Value()*100)/100 +' \\text{ kHz}\\]';}], {fixed:true, visible:true}); | ||
+ | textc=brd2.create('text',[3.2,-0.3, function() | ||
+ | { return '\\[\\phi_1= '+ Math.round(c.Value()*100)/100 +' \\text{ Grad}\\]';}], {fixed:true, visible:true}); | ||
+ | textd=brd2.create('text',[9.9,1.57, function() | ||
+ | { return '\\[A_2= '+ Math.round(d.Value()*100)/100 +' \\text{ V}\\]';}], {fixed:true, visible:true}); | ||
+ | texte=brd2.create('text',[9.9,0.57, function() | ||
+ | { return '\\[f_2= '+ Math.round(e.Value()*100)/100 +' \\text{ kHz}\\]';}], {fixed:true, visible:true}); | ||
+ | textg=brd2.create('text',[9.9,-0.43, function() | ||
+ | { return '\\[\\phi_2= '+ Math.round(g.Value()*100)/100 +' \\text{ Grad}\\]';}], {fixed:true, visible:true}); | ||
+ | textt=brd2.create('text',[3.2,-1.3, function() | ||
+ | { return '\\[t= '+ Math.round(t.Value()*100)/100 +' \\]';}], {fixed:true, visible:true}); | ||
+ | textergebnis1=brd3.create('text',[-0.5,1.5, function() | ||
+ | { 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}); | ||
+ | textergebnis2=brd3.create('text',[1.6,1.5, function() | ||
+ | { 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}); | ||
+ | textergebnis3=brd3.create('text',[4.5,1.5, function() | ||
+ | { 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}); | ||
+ | textergebnis4=brd3.create('text',[7.75,1.5, 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}); | ||
+ | textergebnis5=brd3.create('text',[10.5,1.5, function() | ||
+ | { return '\\[T_0= '+ Math.round(getT0() *100)/100 +' \\]';}], {fixed:true, visible:true, strokeColor:'blue'}); | ||
− | |||
− | + | //Definition der Funktion | |
− | + | signaldarstellung = brd1.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)) | |
− | + | }], {strokeColor: "red"}); | |
− | + | ||
− | + | //Definition des Punktes p_T0, des Hilfspunktes p_T0h und der Geraden l_T0 für Periodendauer T_0 | |
− | }); | + | p_T0=brd1.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) | |
− | + | +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:''}) | |
− | + | p_T0h = brd1.create('point', [function(){ return Math.round(getT0() *100)/100;}, 2], {visible: false, color:"blue", fixed:true, label:false, size:1, name:''}) | |
− | + | l_T0 = brd1.create('line', [p_T0, p_T0h]) | |
− | + | ||
− | + | //Bestimmung des Wertes T_0 mit der Funktion von Siebenwirth | |
+ | function getT0() { | ||
+ | |||
+ | var A, B, C, Q; | ||
+ | if (b.Value() < e.Value()) { | ||
+ | A = b.Value(); | ||
+ | B = e.Value(); | ||
+ | } else { | ||
+ | B = b.Value(); | ||
+ | A = e.Value(); | ||
+ | } | ||
+ | |||
+ | console.log('Berechne T0 mit A=' + A, 'B=' + B); | ||
+ | |||
+ | for (var x = 1; x <= 100; x++) { | ||
+ | C = A / x; | ||
+ | Q = B / C; | ||
+ | console.log(x + '. Durchgang: C = ' + C, 'Q = ' + Q); | ||
+ | if (isInt(Q)) { | ||
+ | console.log('Q ist eine Qanzzahl!!! T0 ist damit ', 1 / C); | ||
+ | return 1 / C; | ||
+ | } | ||
+ | if (x === 10) { | ||
+ | return 10; | ||
+ | } | ||
+ | if ((1/C) > 10) | ||
+ | return 10 | ||
+ | } | ||
+ | } | ||
+ | |||
+ | function isInt(n) { | ||
+ | return n % 1 === 0; | ||
+ | } | ||
+ | |||
+ | |||
+ | |||
+ | //Definition der Funktion zum An- und Ausschalten des Koordinatengitters | ||
+ | function showgrid() { | ||
+ | if (gridbox.checked) { | ||
+ | xaxis = brd1.create('axis', [[0, 0], [1,0]], {}); | ||
+ | yaxis = brd1.create('axis', [[0, 0], [0, 1]], {}); | ||
+ | } else { | ||
+ | xaxis.removeTicks(xaxis.defaultTicks); | ||
+ | yaxis.removeTicks(yaxis.defaultTicks); | ||
+ | } | ||
+ | brd1.fullUpdate(); | ||
+ | }; | ||
+ | </script> | ||
+ | </form> | ||
+ | |||
+ | <script> | ||
+ | //Definition des Reset-Buttons | ||
+ | function zurueck() { | ||
+ | document.getElementById("myForm").reset(); | ||
+ | }; | ||
</script> | </script> | ||
+ | |||
</body> | </body> | ||
</html> | </html> | ||
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Revision as of 22:05, 18 September 2017