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A body executes S.H.M with an amplitude A. At what displacement from the mean position is the potential energy of the body is one fourth of its total energy?

1. A/4
2. A/2
3. 3A/4
4. Some other fraction of A.

Correct answer: A/2

Solution

In SHM, potential energy (PE) is given by (1/2)kx², and total energy (TE) is (1/2)kA². For PE to be one-fourth of TE, (1/2)kx² = (1/4)(1/2)kA². Simplifying, x² = A²/4, so x = A/2.

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