Which characteristic of SHM ensures that the motion repeats exactly after a fixed interval?
**SHM condition** is linear restoring force and inertia producing sinusoidal time dependence. Motions violating a = -ω² x, such as uniform circular motion, are periodic without oscillation about fixed point, highlighting classification criteria for NCERT. The sinusoidal nature of displacement ( x = A cos (ω t + Φ) ) ensures periodicity, as the cosine function repeats every 2π , giving a fixed period T = (2π/ω) . Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E = ½kA² = ½mω²A², result The sinusoidal variation follows, reflecting SHM dependence on amplitude A, ω and system paramet
Ref: NCERT > Physics Book > Oscillations > Periodic Motion and SHM Basic Concepts
