First slide

Simple harmonic motion

Question

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

Moderate

A

$f / 2$
B

$f$
C

$2 f$
D

$4 f$

Solution

Kinetic energy $K = \frac{1}{2} {mv}^{2} = \frac{1}{2} {ma}^{2} ω^{2} \cos^{2} ω t$ $= \frac{1}{4} {mω}^{2} a^{2} (1 + \cos 2 ω t)$ hence kinetic energy varies periodically with double the frequency of S.H.M. i.e. $2 ω$ .

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