ζ = damping ratio = actual / critical
Think of a mass-spring-damper:
m·ẍ + c·ẋ + k·x = 0
c = damping coefficient — force opposing velocity. The faster the mass moves, the harder damping pushes back, always in the counter direction.
k = spring stiffness · m = mass
ζ = c / 2√(km) — the ratio of actual damping to the amount needed for the fastest overshoot-free return (critical damping).
| ζ<1 | Underdamped — oscillates |
| ζ=1 | Critically damped — fastest, no overshoot |
| ζ>1 | Overdamped — slow, no oscillation |