(New page: Given the Signal x(t) = 4sin(2 * pi * 6t), Find the energy and power of the signal from 2 to 6 seconds. [edit] Energy) |
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Given the Signal x(t) = 4sin(2 * pi * 6t), Find the energy and power of the signal from 2 to 6 seconds. | Given the Signal x(t) = 4sin(2 * pi * 6t), Find the energy and power of the signal from 2 to 6 seconds. | ||
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| + | == Energy == | ||
| + | <math>E=\int_2^6 |x(t)|^2 dt</math> | ||
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| + | <math>E=\int_2^6 |4sin(12\pi t)|^2 dt</math> | ||
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| + | |||
| + | <math>E=16*\int_2^6 sin(12\pi t)^2 dt</math> | ||
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| + | <math>E=16*\int_2^6 sin(12\pi t)^2 dt</math> | ||
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| + | <math>E=16*(\dfrac{6 \pi t}{2}-\dfrac{sin(2*(6\pi t))}{4})\mid_1^5</math> | ||
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| + | <math>E=9*(3\pi t-\dfrac{sin(12\pi t)}{4})\mid_1^5</math> | ||
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| + | <math>E=27\pi *t-\dfrac{9sin(12\pi *t)}{4}\mid_1^5</math> | ||
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| + | <math>E=27\pi *5-\dfrac{9sin(12\pi *5)}{4}-(27\pi *1-\dfrac{9sin(12\pi *1)}{4}</math> | ||
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| + | <math>E=\int_1^5 |3sin(6\pi t)|^2 dt=108\pi</math> | ||
Revision as of 08:09, 5 September 2008
Given the Signal x(t) = 4sin(2 * pi * 6t), Find the energy and power of the signal from 2 to 6 seconds.
Energy
$ E=\int_2^6 |x(t)|^2 dt $
$ E=\int_2^6 |4sin(12\pi t)|^2 dt $
$ E=16*\int_2^6 sin(12\pi t)^2 dt $
$ E=16*\int_2^6 sin(12\pi t)^2 dt $
$ E=16*(\dfrac{6 \pi t}{2}-\dfrac{sin(2*(6\pi t))}{4})\mid_1^5 $
$ E=9*(3\pi t-\dfrac{sin(12\pi t)}{4})\mid_1^5 $
$ E=27\pi *t-\dfrac{9sin(12\pi *t)}{4}\mid_1^5 $
$ E=27\pi *5-\dfrac{9sin(12\pi *5)}{4}-(27\pi *1-\dfrac{9sin(12\pi *1)}{4} $
$ E=\int_1^5 |3sin(6\pi t)|^2 dt=108\pi $
