What distinguishes the restoring force in SHM from that in uniform circular motion?
**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). In SHM, the restoring force is linear ( F = -kx ), varying with displacement, while in uniform circular motion, the centripetal force is constant in magnitude and radial. Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E = ½kA² = ½mω²A², result It is linear with respect to displacement follows,
Ref: NCERT > Physics Book > Oscillations > Periodic Motion and SHM Basic Concepts