A body is executing simple harmonic motion with frequency ‘n’, the frequency of its potential energy is :

For a body in simple harmonic motion (SHM) the displacement as a function of time is

where $A$ is the amplitude and $\backslash omega$ is the angular frequency. The ordinary (linear) frequency $n$ is related to the angular frequency by

The potential energy of a harmonic oscillator is

Substituting the displacement gives

Using the trigonometric identity

the potential energy becomes

The term that varies with time is $\backslash cos(2\backslash omega\; t)$. It oscillates with angular frequency $2\backslash omega$, which corresponds to a linear frequency

Therefore the frequency of the potential energy is twice the frequency of the body’s motion.

The correct answer is 2n.