Key Concepts

• • ζ < 1: underdamped — oscillates, overshoots steady state
• • ζ = 1: critically damped — fastest response without overshoot
• • ζ > 1: overdamped — no oscillation, slow approach to steady state
• • Overshoot = e^(−πζ/√(1−ζ²)) × 100% (underdamped only)
• • Settling time t_s ≈ 4/(ζωₙ) for 2% criterion
• • Models spring-mass-dampers, RLC circuits, and control loops