Second-Order Response

Almost every servo, filter and mass-spring-damper behaves like a second-order system near its dominant poles. Overshoot depends only on the damping ratio ζ — not on speed — which is why ζ is the number you design to, and ω_n then sets how fast it all happens.

ζ = 0.707 gives about 4.3% overshoot and is the usual compromise between speed and ringing. Settling time uses the 2% band. Real systems add higher-order poles and dead time, so treat these as the dominant-pole approximation they are.