(→Energy) |
(→Energy) |
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== Energy == | == Energy == | ||
| − | u = (t- | + | <math>u = (t-\pi)</math> |
<math>E=\int_0^{2\pi}{|cos(u)|^2du}</math> | <math>E=\int_0^{2\pi}{|cos(u)|^2du}</math> | ||
| Line 10: | Line 10: | ||
| − | <math>E=\frac{1}{2}((u+\frac{1}{2}sin(2(u)))|_{u=- | + | <math>E=\frac{1}{2}((u+\frac{1}{2}sin(2(u)))|_{u=-\pi}^{u=2\pi-\pi}</math> |
| − | <math>E=\frac{1}{2}( | + | <math>E=\frac{1}{2}(\pi + 0 -(-\pi - 0))</math> |
Revision as of 05:39, 5 September 2008
cos(t-2)
Energy
$ u = (t-\pi) $
$ E=\int_0^{2\pi}{|cos(u)|^2du} $
$ E=\frac{1}{2}\int_0^{2\pi}(1+cos(2(u)))du $
$ E=\frac{1}{2}((u+\frac{1}{2}sin(2(u)))|_{u=-\pi}^{u=2\pi-\pi} $
$ E=\frac{1}{2}(\pi + 0 -(-\pi - 0)) $
$ E=\pi $
Power
$ E=\frac{1}{2\pi-0}\int_0^{2\pi}{|cos(u)|^2du} $
$ =\frac{1}{2\pi-0} *{\frac{1}{2}}\int_0^{2\pi}(1+cos(2u))du $
$ =\frac{1}{4\pi}((t-2)+\frac{1}{2}sin(2u))|_{u=-2}^{u=2\pi-2} $
$ =\frac{1}{4\pi}(2\pi+0-0-0) $
$ =\frac{1}{2} $
