The potential energy of a simple harmonic oscillator when the particle is half way to its end point is (where E is the total energy)

Options

(a) E/8
(b) E/4
(c) E/2
(d) 2E/3

Correct Answer:

E/4

Explanation:

P.E. = (1/2) mω²y² ⇒ At y = a/2 ⇒ (1/2) (mω²a²/4)
Total energy (E) = P.E. at extreme position = (1/2) mω²a²
P.E. = (1/4).[(1/2) mω²a²] = E/4