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<math>=\frac{1}{2} + \frac{1}{40 \pi^2} sin(20 \pi^2)</math> | <math>=\frac{1}{2} + \frac{1}{40 \pi^2} sin(20 \pi^2)</math> | ||
| + | |||
| + | == Sources == | ||
| + | |||
| + | <font size="3">Lecure notes</font> | ||
Revision as of 13:46, 4 September 2008
Contents
Equation
$ x(t) = cos(2 \pi t) $ from $ 0 $ to $ 5 \pi $
Energy
$ E = \int_{0}^{5 \pi}{|cos(2 \pi t)|^2dt} $
$ = \int_{0}^{5 \pi}{[1 + cos(4 \pi t)]dt} $
$ =\frac{5 \pi}{2} + \frac{1}{8 \pi} sin(20 \pi^2) $
Power
$ P = \frac{1}{5 \pi - 0} \int_{0}^{5 \pi}{|cos(2 \pi t)|^2dt} $
$ = \frac{1}{5 \pi} \int_{0}^{5 \pi}{[1 + cos(4 \pi t)]dt} $
$ =\frac{1}{2} + \frac{1}{40 \pi^2} sin(20 \pi^2) $
Sources
Lecure notes
