Simple Harmonic Motion

An oscillating body moves repeatedly about an equilibrium or mean position. Not every oscillation is SHM. For motion to be simple harmonic: a ∝ −x Therefore: a = −ω²x where: `a` = acceleration `x` = displacement from equilibrium `ω` = angular frequency The negative sign shows that acceleration is always opposite to displacement. `x = 0` Therefore: `a = 0` Speed is maximum.

`x = ±A` Acceleration magnitude is maximum. Speed is zero.

Using `F = ma`: **F = −mω²x** Thus restoring force is also proportional to displacement and directed toward equilibrium.

**a = −ω²x F = −mω²x x = A cos(ωt+φ) ω = 2πf = 2π/T**