simple harmonic motion

The motion governed by `ẍ = −ω²x` for some constant `ω > 0`. Its solutions are sinusoidal: `x(t) = A cos(ωt + φ)`, with constant period `T = 2π/ω` independent of amplitude `A`. A spring obeying Hooke's law produces it exactly. A pendulum produces it _only_ in the small-angle limit, after `sin θ` has been replaced by `θ`. Most "oscillator" intuitions in physics, engineering, and signal processing live inside this single equation.