Practice question

**Periodic motion** repeats after fixed period T, x(t+T)=x(t), while oscillatory motion involves to-and-fro about equilibrium. SHM is special periodic motion where restoring force proportional to displacement, F = -k x, acceleration a = -ω² x, leading to sinusoidal displacement x = A cos(ωt + φ). Velocity: v = -ω A sin (ω t + Φ) . A = 3 m, ω = 4π s⁻¹, Φ = (π/3) . At t = 0 : v = -4π × 3 sin (π/3) = -12π × (√(3)/2) ≈ -32.58 m/s . Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and