Answer: kA²/4.
- A kA²/4
- B kA²/2
- C kA²
- D kA²/8
Correct answer: A. kA²/4
Explanation: PE = (1/2)kA² sin²(ωt). Average of sin² over a full cycle = 1/2. So avg PE = (1/2)kA² × (1/2) = kA²/4. Same as average KE.
In SHM, displacement and velocity are 90° out of phase (v is maximum when x=0, and zero when x is extreme), while acceleration is always exactly opposite in sign to displacement, consistent with a = −ω²x.
Concept context
Simple harmonic motion, spring-mass, pendulum, energy in SHM, and resonance.