Simple Harmonic Motion

A motion that repeats continuously on

A motion that repeats continuously on a definite path in a definite interval of time is periodic motion. The interval is called the time period, T. Ex

A periodic motion in which

A periodic motion in which a body moves to and fro about a definite mean or equilibrium position, confined between extreme positions, is oscillatory m

SHM is harmonic oscillation of constant

SHM is harmonic oscillation of constant amplitude and single frequency. In SHM, the acceleration or force is directly proportional to displacement and

Amplitude

Amplitude, a, is the maximum displacement from equilibrium and equals the radius of the reference circle. Angular frequency, ω, is given by T = 2π/ω a

The displacement may be written as

The displacement may be written as y = a sin(ωt + φ). The velocity is v = ω√(a² − y²), the acceleration is α = −ω²y, and the differential equation is