The function sin^2 ,( t) represents - Vidyadip

MCQ

The function $sin^2\,(\omega t)$ represents

✓
a simple harmonic motion with a period $\frac{\pi }{\omega }$
B
a periodic, but not simple harmonic motion with a period $\frac{2\pi }{\omega }$
C
a periodic, but not simple harmonic motion with a period $\frac{\pi }{\omega }$
D
a simple harmonic motion with a period $\frac{2\pi }{\omega }$

✓

Answer

Correct option: A.

a simple harmonic motion with a period $\frac{\pi }{\omega }$

a
Clearly $\sin ^{2} \omega t$ is a periodic function as $sin\, \omega t$ is periodic with period $\pi / \omega$

For $SHM$ $\frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{dt}^{2}} \propto-\mathrm{y}$

$\frac{\mathrm{dy}}{\mathrm{dt}}=2 \omega \sin \omega t \cos \omega t=\omega \sin 2 \omega t$

$\frac{d^{2} y}{d t^{2}}=2 \omega^{2} \cos 2 \omega t$ which is not proporti-

onal $to - y.$ Hence it is not in $SHM.$

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