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We will find the energy in one cycle of the cosine waveform. | We will find the energy in one cycle of the cosine waveform. | ||
| − | <math>E=\int_0^{2\pi}{| | + | <math>E=\int_0^{2\pi}{|2cos(t)|^2dt}</math> |
| + | <math>=\int_0^{2\pi}{(2(2cos(t)^2-1)+2)dt}</math> | ||
| − | <math>= | + | <math>=\int_0^{2\pi}{2+cos(2t))dt</math> |
| + | <math>=(2t+sin(2t))|_{t=0}^{t=2\pi}</math> | ||
| − | <math>=\ | + | <math>=(4\pi+0-0-0)</math> |
| − | + | <math>=4\pi</math> | |
| − | + | ||
| − | + | ||
| − | + | ||
| − | <math>=\pi</math> | + | |
Revision as of 15:41, 3 September 2008
Signal
$ y(t)=2cos(t) $
Energy
We will find the energy in one cycle of the cosine waveform.
$ E=\int_0^{2\pi}{|2cos(t)|^2dt} $
$ =\int_0^{2\pi}{(2(2cos(t)^2-1)+2)dt} $
$ =\int_0^{2\pi}{2+cos(2t))dt $
$ =(2t+sin(2t))|_{t=0}^{t=2\pi} $
$ =(4\pi+0-0-0) $
$ =4\pi $
