MCQ
A particle moves on $x-$ axis according to the equation $x = x_0\,\,sin^2\,\omega t,$ the motion is simple harmonic
- AWith amplitude $x_0$
- BWith amplitude $2x_0$
- CWith time period $(2\pi /\omega )$
- ✓With time period $(\pi /\omega )$
✓
Answer
Correct option: D.
With time period $(\pi /\omega )$
d
$\mathrm{x}=\mathrm{x}_{0} \sin ^{2} \omega \mathrm{t}$
$\mathrm{x}=\mathrm{x}_{0} \sin ^{2} \omega \mathrm{t}$
$x=x_{0}\left[\frac{1-\cos 2 \omega t}{2}\right]=\frac{x_{0}}{2}-\frac{x_{0} \cos 2 \omega t}{2}$
Angular Frequency $=2 \omega$
$\frac{2 \pi}{\mathrm{T}}=2 \omega$
$\mathrm{T}=\frac{\pi}{\omega}$
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