HW1.5 Miles Whittaker - Energy and Power ECE301Fall2008mboutin - Rhea

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