Question

A body executing SHM has displacement \( y = A \cos \omega t \). Identify the graph which represents the variation of potential energy (PE) as a function of time \( t \) and displacement.

• A. I
• B. II
• C. III
• D. IV

Hint:

In SHM, potential energy varies as the square of displacement, and it has a periodic behavior.

Answer 1

The Correct Option is B

Step 1: Relationship between potential energy and displacement.
The potential energy \( PE \) in SHM is proportional to the square of the displacement, given by: \[ PE = \frac{1}{2} k x^2 \] where \( x \) is the displacement and \( k \) is the spring constant.

Step 2: Graph of potential energy.
Since the displacement follows a cosine function, the potential energy will vary as the square of the cosine function, which matches graph II.