Question

A particle moves on x-axis according to the equation $x=x_{0}\sin^{2} \omega t$ , the motion is simple harmonic

• A. with amplitude $x_{0}$
• B. with amplitude $2x_{0}$
• C. with time period $\left(\frac{2 \pi }{\omega }\right)$
• D. with time period $\left(\frac{\pi }{\omega }\right)$

Answer 1

Answer: (D)

$x=x_0 \sin ^2 \omega t=\frac{x_0}{2}(1-\cos 2 \omega t)=\frac{x_0}{2}-\frac{x_0}{2} \cos 2 \omega t$
Frequency $\omega '=2\omega $
$\Rightarrow \frac{2 \pi }{T'}=2 \, \omega $
$\Rightarrow T'=\left(\frac{\pi }{\omega }\right)$
Amplitude = $\frac{x_{0}}{2}$