(→Calculating the Energy of a Function) |
(→Calculating the Power of a Function) |
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| − | <math>=\int_0^{2\pi}(1-cos(2t))dt</math> | + | <math>E=\int_0^{2\pi}(1-cos(2t))dt</math> |
| − | <math>=(t-\frac{1}{2}sin(2t))|_{t=0}^{t=2\pi}</math> | + | <math>E=(t-\frac{1}{2}sin(2t))|_{t=0}^{t=2\pi}</math> |
| − | <math>=2\pi)</math> | + | <math>E= 2{\pi}</math> |
| + | |||
| + | == Calculating the Power of a Function == | ||
| + | |||
| + | After you have the energy of a function, calculating the power isn't very difficult. Use the following equation. | ||
| + | |||
| + | <math>E=\frac{1}{t_2 - t_1}\int_{t1}^{t2}{|f(x)|^2}</math> | ||
| + | |||
| + | For our previous example, continue by following below. | ||
| + | |||
| + | <math>E=\frac{1}{2{\pi} - 0}\int_{t1}^{t2}{|f(x)|^2}</math> | ||
| + | |||
| + | <math>E=\frac{1}{2{\pi} - 0}*{2\pi}</math> | ||
| + | |||
| + | <math>E= 1 | ||
Latest revision as of 16:07, 5 September 2008
Calculating the Energy of a Function
To calculate the energy of a function, use the following equation.
$ E=\int_{t1}^{t2}{|f(t)|^2dt} $
For clarity, follow the example below.
$ E=\int_{0}^{2\pi}{|2sin(t)|^2dt} $
$ E=2\int_{0}^{2\pi}{|sin(t)|^2dt} $
$ E=\int_0^{2\pi}(1-cos(2t))dt $
$ E=(t-\frac{1}{2}sin(2t))|_{t=0}^{t=2\pi} $
$ E= 2{\pi} $
Calculating the Power of a Function
After you have the energy of a function, calculating the power isn't very difficult. Use the following equation.
$ E=\frac{1}{t_2 - t_1}\int_{t1}^{t2}{|f(x)|^2} $
For our previous example, continue by following below.
$ E=\frac{1}{2{\pi} - 0}\int_{t1}^{t2}{|f(x)|^2} $
$ E=\frac{1}{2{\pi} - 0}*{2\pi} $
$ E= 1 $
