Practice question

**Angular SHM** of pendulum results from restoring torque τ = -m g L sinθ ≈ -m g L θ for small θ, analogous to linear SHM with ω = √(g/L). This relation allows period determination from length and local gravity, illustrating gravitational influence on oscillation. Period: T = (1/v) = (1/0.4) = 2.5 s . T = 2π √((L/g)) ⇒ 2.5 = 2π √((L/9.8)) . √((L/9.8)) = (2.5/2π) ≈ 0.398 ⇒ (L/9.8) = (0.398)² ⇒ L ≈ 1.55 m . Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E = ½kA² = ½mω²A², result 1.55 m