First slide

Simple hormonic motion

Question

A particle executes simple harmonic motion with a frequency f. The frequency with which its kinetic energy oscillates is

Moderate

A

$\frac{f}{2}$
B

f
C

2f
D

4f

Solution

Kinetic energy $K = \frac{1}{2} {mv}^{2} = \frac{1}{2} {ma}^{2} ω^{2} \cos^{2} ωt = \frac{1}{2} {mω}^{2} a^{2} (1 + \cos 2 ωt)$ hence kinetic energy varies periodically with double the frequency of S.H.M. i.e., 2f.

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