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| − | <math>E=\frac{1}{2\pi-0}\ | + | <math>E=\frac{1}{2\pi-0}\int_{-2}^{2\pi-2}{|cos(u)|^2du}</math> |
| − | <math>=\frac{1}{2\pi-0} *{\frac{1}{2}}\ | + | <math>=\frac{1}{2\pi-0} *{\frac{1}{2}}\int_{-2}^{2\pi-2}(1+cos(2u))du</math> |
| − | <math>=\frac{1}{4\pi}((u)+\frac{1}{2}sin(2u))|_{u=- | + | <math>=\frac{1}{4\pi}((u)+\frac{1}{2}sin(2u))|_{u=-2}^{u=2\pi-2}</math> |
| − | <math>=\frac{1}{4\pi}(\pi+ | + | <math>=\frac{1}{4\pi}(2\pi-2+.378-(-2+.378))</math> |
<math>=\frac{1}{2}</math> | <math>=\frac{1}{2}</math> | ||
Revision as of 05:51, 5 September 2008
cos(t-2)
Energy
A time shift should not effect the energy of a function.
$ u = (t-2) $
$ E=\int_{-2}^{2\pi-2}{|cos(u)|^2du} $
$ E=\frac{1}{2}\int_{-2}^{2\pi-2}(1+cos(2(u)))du $
$ E=\frac{1}{2}((u+\frac{1}{2}sin(2(u)))|_{u=-2}^{u=2\pi-2} $
$ E=\frac{1}{2}(2\pi-2 + .378 -(-2 - .378)) $
$ E=\pi $
Power
$ E=\frac{1}{2\pi-0}\int_{-2}^{2\pi-2}{|cos(u)|^2du} $
$ =\frac{1}{2\pi-0} *{\frac{1}{2}}\int_{-2}^{2\pi-2}(1+cos(2u))du $
$ =\frac{1}{4\pi}((u)+\frac{1}{2}sin(2u))|_{u=-2}^{u=2\pi-2} $
$ =\frac{1}{4\pi}(2\pi-2+.378-(-2+.378)) $
$ =\frac{1}{2} $
