What fundamental property of the restoring force distinguishes simple harmonic motion from other oscillatory motions?
**General equation of SHM** x = A sin(ωt + φ) or A cos(ωt + φ) includes amplitude A (m), angular frequency ω = √(k/m) (rad/s) for spring system, and initial phase φ (rad) setting t=0 position. Phase (ωt + φ) determines instantaneous state, phase difference Δφ governs interference of two SHM motions. In SHM, the restoring force must be directly proportional to displacement and opposite in direction ( F = -kx ), ensuring a linear relationship, unlike non-linear oscillatory systems. Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E = ½kA² = ½mω²A², result Its linearity
Ref: NCERT > Physics Book > Oscillations > Equations of SHM, Phase and Angular Frequency