Free Overshoot Calculator
Calculate the percent overshoot and peak time of a second-order underdamped system step response.
Percent Overshoot
37.23 %
Percent Overshoot vs Damping Ratio (zeta)
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.
Example Calculation
A system with zeta = 0.3, omega_n = 10 rad/s.
- 01omega_d = 10 × sqrt(1 - 0.09) = 10 × 0.9539 = 9.539 rad/s
- 02%OS = 100 × exp(-pi × 0.3 / 0.9539)
- 03%OS = 100 × exp(-0.9874) = 100 × 0.3730 = 37.30%
- 04Peak time = pi / 9.539 = 0.3293 s
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