Question

When particle oscillates simple harmonically its potential energy varies periodically. If frequency of the particle is n, the frequency of the potential energy is

• A. n/2
• B. n
• C. 2n
• D. 4n

Answer 1

Answer: (C)

2n

$PE=\frac{1}{2}m{\omega }^2{x}^2=\frac{1}{2}m{\omega }^2\left(x_0^2{\sin }^2\omega t\right)=\frac{1}{2}m{\omega }^2{x}_0^2\left(\frac{1-\cos 2\omega t}{2}\right)=\frac{1}{4}m{\omega }^2{x}_0^2-\frac{1}{4}m{\omega }^2{x}_0^2\cos 2\omega t$
frequency of above equation i.e. frequency of P.E. is $2\omega$ or $2n$