(→Equation) |
(→Sources) |
||
| (10 intermediate revisions by the same user not shown) | |||
| Line 1: | Line 1: | ||
== Equation == | == Equation == | ||
| − | <math>x(t) = cos( | + | <font size="3"><math>x(t) = cos(2 \pi t)</math> from <math>0</math> to <math>5 \pi</math></font> |
== Energy == | == Energy == | ||
| − | <math>E = </math> | + | <math>E = \int_{0}^{5 \pi}{|cos(2 \pi t)|^2dt}</math> |
| + | |||
| + | <math>= \int_{0}^{5 \pi}{[1 + cos(4 \pi t)]dt}</math> | ||
| + | |||
| + | <math>=\frac{5 \pi}{2} + \frac{1}{8 \pi} sin(20 \pi^2)</math> | ||
== Power == | == Power == | ||
| + | |||
| + | <math>P = \frac{1}{5 \pi - 0} \int_{0}^{5 \pi}{|cos(2 \pi t)|^2dt}</math> | ||
| + | |||
| + | <math>= \frac{1}{5 \pi} \int_{0}^{5 \pi}{[1 + cos(4 \pi t)]dt}</math> | ||
| + | |||
| + | <math>=\frac{1}{2} + \frac{1}{40 \pi^2} sin(20 \pi^2)</math> | ||
| + | |||
| + | == Sources == | ||
| + | |||
| + | <font size="3">Lecture Notes</font> | ||
Latest revision as of 13:47, 4 September 2008
Contents
Equation
$ x(t) = cos(2 \pi t) $ from $ 0 $ to $ 5 \pi $
Energy
$ E = \int_{0}^{5 \pi}{|cos(2 \pi t)|^2dt} $
$ = \int_{0}^{5 \pi}{[1 + cos(4 \pi t)]dt} $
$ =\frac{5 \pi}{2} + \frac{1}{8 \pi} sin(20 \pi^2) $
Power
$ P = \frac{1}{5 \pi - 0} \int_{0}^{5 \pi}{|cos(2 \pi t)|^2dt} $
$ = \frac{1}{5 \pi} \int_{0}^{5 \pi}{[1 + cos(4 \pi t)]dt} $
$ =\frac{1}{2} + \frac{1}{40 \pi^2} sin(20 \pi^2) $
Sources
Lecture Notes
