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 √(A² - x²) . A = 3 m, ω = 2 s⁻¹, x = 1.5 m . v = 2 √(3² - 1.5²) = 2 √(9 - 2.25) = 2 √(6.75) ≈ 5.2 m/s . Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E = ½kA²