Overshoot Calculator

Calculate the percent overshoot and peak time of a second-order underdamped system step response.

rad/s

Percent Overshoot

37.23 %

Peak Time0.3293 s
Damped Frequency9.539 rad/s

Percent Overshoot vs Damping Ratio (zeta)

Vedi formula →

Formula

## 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.

Esempio Risolto

A system with zeta = 0.3, omega_n = 10 rad/s.

  1. 01omega_d = 10 × sqrt(1 - 0.09) = 10 × 0.9539 = 9.539 rad/s
  2. 02%OS = 100 × exp(-pi × 0.3 / 0.9539)
  3. 03%OS = 100 × exp(-0.9874) = 100 × 0.3730 = 37.30%
  4. 04Peak time = pi / 9.539 = 0.3293 s