Overshoot Calculator — Formule
## Second-Order Overshoot
Overshoot is the amount by which the step response exceeds the final steady-state value, expressed as a percentage. It depends only on the damping ratio.
### Formula
**%OS = 100 × exp(-pi × zeta / sqrt(1 - zeta²))**
**Peak time: tp = pi / omega_d**, where omega_d = omega_n × sqrt(1 - zeta²) is the damped natural frequency.
For zeta = 0 (undamped), overshoot is 100%. For zeta >= 1 (critically damped or overdamped), there is no overshoot.
Overshoot is the amount by which the step response exceeds the final steady-state value, expressed as a percentage. It depends only on the damping ratio.
### Formula
**%OS = 100 × exp(-pi × zeta / sqrt(1 - zeta²))**
**Peak time: tp = pi / omega_d**, where omega_d = omega_n × sqrt(1 - zeta²) is the damped natural frequency.
For zeta = 0 (undamped), overshoot is 100%. For zeta >= 1 (critically damped or overdamped), there is no overshoot.
Exemple Résolu
A system with zeta = 0.3, omega_n = 10 rad/s.
- omega_d = 10 × sqrt(1 - 0.09) = 10 × 0.9539 = 9.539 rad/s
- %OS = 100 × exp(-pi × 0.3 / 0.9539)
- %OS = 100 × exp(-0.9874) = 100 × 0.3730 = 37.30%
- Peak time = pi / 9.539 = 0.3293 s