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<math>9*\int_1^5 sin(6\pi t)^2 dt</math> | <math>9*\int_1^5 sin(6\pi t)^2 dt</math> | ||
| − | <math>9*(\dfrac{6 \pi t}{2}-\dfrac{sin(2*(6\pi | + | <math>9*(\dfrac{6 \pi t}{2}-\dfrac{sin(2*(6\pi t))}{4})</math>evaluated at 5 and 1 |
| − | <math>9*(3\pi | + | <math>9*(3\pi t-\dfrac{sin(12\pi t)}{4})</math>evaluated at 5 and 1 |
| − | <math>27\pi *t- | + | <math>27\pi *t-\dfrac{9sin(12\pi *t)}{4}</math>evaluated at 5 and 1 |
| − | <math>27\pi *5- | + | <math>27\pi *5-\dfrac{9sin(12\pi *5)}{4}-(27\pi *1-\dfrac{9sin(12\pi *1)}{4}</math> |
<math>\int_1^5 |3sin(6\pi t)|^2 dt=108\pi | <math>\int_1^5 |3sin(6\pi t)|^2 dt=108\pi | ||
Revision as of 08:20, 4 September 2008
Given the Signal $ x(t)=3sin(2*pi*3t) $, Find the energy and power of the signal from 0 to 5 seconds.
Power
$ \int_1^5 |x(t)|^2 dt $
$ \int_1^5 |3sin(6\pi t)|^2 dt $
$ 9*\int_1^5 sin(6\pi t)^2 dt $
$ 9*\int_1^5 sin(6\pi t)^2 dt $
$ 9*(\dfrac{6 \pi t}{2}-\dfrac{sin(2*(6\pi t))}{4}) $evaluated at 5 and 1
$ 9*(3\pi t-\dfrac{sin(12\pi t)}{4}) $evaluated at 5 and 1
$ 27\pi *t-\dfrac{9sin(12\pi *t)}{4} $evaluated at 5 and 1
$ 27\pi *5-\dfrac{9sin(12\pi *5)}{4}-(27\pi *1-\dfrac{9sin(12\pi *1)}{4} $
$ \int_1^5 |3sin(6\pi t)|^2 dt=108\pi $
