First slide

Simple harmonic motion

Question

The function $\sin^{2} (ωt)$ represents

Moderate

A

A simple harmonic motion with a period $2 π / ω$
B

A simple harmonic motion with a period $π / ω$
C

A periodic but not simple harmonic motion with a period $2 π / ω$
D

A periodic but not simple harmonic, motion with a period $π / ω$

Solution

$y = \sin^{2} ω t = \frac{1 - \cos 2 ωt}{2} \Rightarrow$ Period, $T = \frac{2 π}{2 ω} = \frac{π}{ω}$
The given function is not satisfying the standard differential equation of S.H.M. $\frac{d^{2} y}{{dx}^{2}} = - ω^{2} y$ . Hence it represents periodic motion but not S.H.M.

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