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(→Power) |
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== x(t) = sin t == | == x(t) = sin t == | ||
== Energy == | == Energy == | ||
| − | <math>E=\int_0^{2\pi}{|sin(t)|^2dt}</math><br> | + | <math>E=\int_0^{2\pi}{|sin(t)|^2dt}</math><br><br> |
| − | <math>=\frac{\int_0^{2\pi}(1-cos(2t))dt}{2}</math><br> | + | <math>=\frac{\int_0^{2\pi}(1-cos(2t))dt}{2}</math><br><br> |
| − | <math>=\frac{t-\frac{1}{2}sin(2t)}{2}|_{t=0}^{t=2\pi}</math><br> | + | <math>=\frac{t-\frac{1}{2}sin(2t)}{2}|_{t=0}^{t=2\pi}</math><br><br> |
| − | <math>\frac{1}{2}(2\pi-0-0+0)</math><br> | + | <math>=\frac{1}{2}(2\pi-0-0+0)</math><br><br> |
| − | <math>\pi</math> | + | '''<math>=\pi</math>''' |
| + | |||
| + | == Power == | ||
| + | <math>P=\frac{1}{2\pi-0}\int_0^{2\pi}{|sin(t)|^2dt}</math><br><br> | ||
| + | <math>P=\frac{1}{2\pi}E</math><br><br> | ||
| + | <math>P=\frac{1}{2\pi}\pi</math><br><br> | ||
| + | <math>P=\frac{1}{2}</math><br><br> | ||
Latest revision as of 18:38, 2 September 2008
x(t) = sin t
Energy
$ E=\int_0^{2\pi}{|sin(t)|^2dt} $
$ =\frac{\int_0^{2\pi}(1-cos(2t))dt}{2} $
$ =\frac{t-\frac{1}{2}sin(2t)}{2}|_{t=0}^{t=2\pi} $
$ =\frac{1}{2}(2\pi-0-0+0) $
$ =\pi $
Power
$ P=\frac{1}{2\pi-0}\int_0^{2\pi}{|sin(t)|^2dt} $
$ P=\frac{1}{2\pi}E $
$ P=\frac{1}{2\pi}\pi $
$ P=\frac{1}{2} $
