Question

A particle of mass $M$ is executing oscillations about the origin on the x-axis. Its potential energy is $|U|=K|x^2|$ where $K$ is a positive constant. If the amplitude of oscillations is $a$, then its period $T$ is

• A. proportional to $1/\sqrt{a}$
• B. independent of $a$
• C. proportional to $\sqrt{a}$
• D. proportional to $a^{1/2}$

Answer 1

Answer: (B)

independent of $a$

The restoring force is $-m{\omega }^{2}x=-dU/dx=-2Kx\Rightarrow \omega =\sqrt{2K/m}$ where $\omega$ is the angular frequency of SHM.

Time period $T=2\pi /\omega =2\pi \sqrt{m/2K}$

So Time period is independent of amplitude $a$.