Answer: -mgL sinθ ≈ -mgLθ.
- A -mgL sinθ ≈ -mgLθ
- B mgLθ in standard practice
- C -mLθ under most conditions encountered
- D -mgL cosθ as frequently observed in practice
Correct answer: A. -mgL sinθ ≈ -mgLθ
Explanation: Torque = -mg sinθ × L ≈ -mgLθ (for small θ). This gives α = -(g/L)θ, so ω² = g/L and T = 2π√(L/g).
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.