Question

A particle moves on x-axis according to the equation $x=x_{0}si{n}^{2}wt$, the motion is simple harmonic,

• A. $withamplitude=\frac{x_0}{2}$
• B. $withamplitude=2x_0$
• C. $withtimeperiod\frac{2\pi }{\omega }$
• D. $withtimeperiod\frac{3\pi }{\omega }$

Answer 1

The correct option is A

$withamplitude=\frac{x_0}{2}$

$x=x_{0}si{n}^2\omega t$

$=\frac{x_0}{2}(1-cos2\omega t)=\frac{x_0}{2}-\frac{x_0}{2}cos2\omega t$

Frequency ${\omega }^{\prime }=2\omega$

$\Rightarrow \frac{2\pi }{T^{\prime }}=2\omega$

$\Rightarrow T^{\prime }=\left(\frac{\pi }{\omega }\right)$

$Amplitude=\frac{x_0}{2}$