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The potential energy of a simple harmonic oscillator when the particle is halfway to its end point is

1. 1/2 E
2. 2/3 E
3. 1/8 E
4. 1/4 E

Correct answer: 1/2 E

Solution

In simple harmonic motion, the potential energy (U) is proportional to the square of the displacement (x²). At halfway to the endpoint (amplitude A), the displacement is A/2. Thus, U = (1/2)k(A/2)² = (1/4)(1/2)kA² = (1/2)E, where E is the total energy.

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