Oscillations - Result Question 10
13. The displacement of a particle along the $x$-axis is given by $x=a \sin ^{2} \omega t$. The motion of the particle corresponds to:
[2010]
(a) simple harmonic motion of frequency $\omega / \pi$
(b) simple harmonic motion of frequency $3 \omega / 2 \pi$
(c) non simple harmonic motion
(d) simple harmonic motion of frequency $\omega / 2 \pi$
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Answer:
Correct Answer: 13. (a)
Solution:
- (a) $x=a \sin ^{2} \omega t=\frac{a}{2}(1-\cos 2 \omega t)$
$\frac{d x}{d t}=\frac{a}{2} 2 \omega \sin 2 \omega t$
$\Rightarrow \frac{d^{2} x}{d t^{2}}=\frac{4 \omega^{2} a}{2} \cdot \cos 2 \omega t$
This represents an S. H. M. of frequency
$=\frac{\omega}{\pi}$
