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Classical Mechanics

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Mechanical Energy: Speed of a Pendulum

CLMECH-FXJ07J

A pendulum, consisting of a mass $m$ on the end of a very light rod of length $L$, swings back and forth.

If the mass is raised to an initial angle $\theta_o$ relative to the vertical, which of the expressions below gives the speed of the mass as a function of the angle from the vertical?

A

$v=\sqrt{2\,g\,L\left[\cos(\theta)-\cos(\theta_o)\right]}$

B

$v=\sqrt{2\,g\,L\left[\cos(\theta_o)-\cos(\theta)\right]}$

C

$v=\sqrt{2\,m\,g\,L\left[\cos(\theta)-\cos(\theta_o)\right]}$

D

$v=2\,g\,L\left[\cos(\theta)-\cos(\theta_o)\right]$