Simple Harmonic Motion (SHM)

Definition

The purest back-and-forth vibration — a mass on a spring, or a pendulum swinging through small angles, repeats the same motion indefinitely.

$x = A\cos(\omega t + \phi)$

Technical definition

Motion with restoring force F = −kx gives x(t) = A cos(ωt + φ), with ω = √(k/m) and period T = 2π√(m/k).

Example

A 0.5 kg mass on a 20 N/m spring oscillates with period 2π√(0.5/20) ≈ 0.99 s — about one full swing per second.

Common confusion

SHM requires the restoring force to be proportional to displacement. A bouncing ball is periodic but NOT simple harmonic — gravity there is constant, not proportional to position.