Physics

Problem

74. Pendulum Velocity vs. Position A pendulum that swings toward and away from a motion detector has a distance (in feet) from the detector of

x(t)=5+3 \sin (\pi t+\pi / 2)

and a velocity (in

\mathrm{ft} / \mathrm{sec}

) of

y(t)=3 \pi \cos (\pi t+\pi / 2)

, where

t

represents time (in seconds). (a) Prove that the plot of velocity versus position (distance) is an ellipse. (b) Writing to Learn Describe the motion of the pendulum.

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