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==Energy== | ==Energy== | ||
| − | Energy of cos(2t) from t= 0 to 2 | + | Energy of cos(2t) from t= 0 to <math>2\pi</math> |
| − | <math>E = \int_{ | + | <math>E = \int_{t1}^{t2}{|(f(t)|^2}dt</math> |
| − | <math>E = | + | <math>E = \int_{0}^{2\pi}{|cost(2t)|^2}dt</math> |
| − | <math>E = | + | <math>E = \frac{1}{2} \int_{0}^{2\pi}{|cost(4t)|^2}dt</math> |
| − | <math>E = 2</math> | + | <math>E = \frac{1}{2} (t + \frac{1}{4}(sin(4t))| t= 0 to 2\pi</math> |
| + | |||
| + | <math>E = \frac{1}{2} (2\pi + 0)</math> | ||
| + | |||
| + | <math>E = \pi</math> | ||
==Power== | ==Power== | ||
Power of cos(2t) | Power of cos(2t) | ||
| − | <math>P = \frac{1}{t2-t1}\int_{ | + | <math>P = \frac{1}{t2-t1}\int_{t1}^{t2}{|f(t)|^2}dt</math> |
| + | |||
| + | <math>P = \frac{1}{2\pi-0}\int_{0}{2\pi}{|cos(2t)|^2}dt</math> | ||
| + | |||
| + | <math>P = \frac{1}{2\pi} * E</math> | ||
| + | |||
| + | <math>P = \frac{1}{2\pi} * \pi</math> | ||
| + | |||
| + | <math>P = \frac{1}{2}</math> | ||
Latest revision as of 10:53, 5 September 2008
Energy
Energy of cos(2t) from t= 0 to $ 2\pi $
$ E = \int_{t1}^{t2}{|(f(t)|^2}dt $
$ E = \int_{0}^{2\pi}{|cost(2t)|^2}dt $
$ E = \frac{1}{2} \int_{0}^{2\pi}{|cost(4t)|^2}dt $
$ E = \frac{1}{2} (t + \frac{1}{4}(sin(4t))| t= 0 to 2\pi $
$ E = \frac{1}{2} (2\pi + 0) $
$ E = \pi $
Power
Power of cos(2t)
$ P = \frac{1}{t2-t1}\int_{t1}^{t2}{|f(t)|^2}dt $
$ P = \frac{1}{2\pi-0}\int_{0}{2\pi}{|cos(2t)|^2}dt $
$ P = \frac{1}{2\pi} * E $
$ P = \frac{1}{2\pi} * \pi $
$ P = \frac{1}{2} $
