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
• B. With amplitude
• C. With time period
• D. With time period

Answer 1

The correct option is D With time period

$x=x_{0}si{n}^2\omega t=\frac{x_0}{2}(1-cos2\omega t)=\frac{x_0}{2}-\frac{x_0}{2}cos2\omega tFrequency{\omega }^{{}^{\prime }}=2\omega \Rightarrow \frac{2\pi }{T^{{}^{\prime }}}=2\omega \Rightarrow T^{{}^{\prime }}=\left(\frac{\pi }{\omega }\right)Amplitude=\frac{x_0}{2}$