Skip to main content
Physics Guru is an online education and competitive examinations preparation portal founded by Manish Verma, an IIT Madras alumnus, providing learning resources for competitive examinations.

The emphasis is on conceptual understanding, analytical thinking and problem solving rather than simply memorising formulas and standard methods.

The objective is to help students understand what they are learning and develop the ability to solve problems they have not seen before.

Frequency of potential energy in SHM = ?

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

(1) n                   (2) 2n
(3) 3n                 (4) 4n

Solution

In SHM, the potential energy is maximum at extreme positions and minimum at mean position. There are two extreme positions in one cycle and two mean positions. So, the time period should be halved or frequency should be doubled.

Alternate Solution

Potential Energy $U = \frac{1}{2}m{\omega ^2}{A^2}{\sin ^2}(\omega t + \phi )$

Or $U \propto {\sin ^2}(\omega t + \phi )$

Sin function alternates above and below x-axes whereas square of Sin function cannot be negative. So, the region below x-axis of Sin function is folded upwards above x-axes when it is squared. Thus the frequency is doubled or the time period is halved.

Answer: (2)