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). Displacement ( x = A cos (ω t + Φ) ) and acceleration ( a = -ω² A cos (ω t + Φ) ) are 180° ( π radians) out of phase, as acceleration is the negative of displacement. Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E = ½kA² =