Simple Harmonic Motion — Formula Sheet

a = -ω²x

T = 2π√(m/k)

T = 2π√(l/g)

ω = √(k/m)

v_max = Aω

K = ½mω²(A² - x²)

U = ½kx²

E = ½kA²

SHM occurs when acceleration is proportional to displacement and opposite in direction: a ∝ -x.

The general equation of SHM is y = A sin(ωt + φ) or y = A cos(ωt + φ).

Frequency (f)

Number of oscillations per second, f = 1/T.

Time period of spring-mass system

T = 2π√(m/k).

In SHM, acceleration ∝ displacement and is directed toward the mean position.