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Second-Order Response

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Calculate damping ratio response metrics such as overshoot, settling time, and damped natural frequency.

rad/s
zeta
%

Settling time

1.09 s

2.0% final-value band

Overshoot

20.53 %

underdamped

Damped natural frequency

7.14 rad/s

oscillation rate when underdamped

Calculation breakdown

Peak time0.44 s
Peak response1.205
Decay rate3.60 1/s
Damping time constant0.28 s
Response at settling estimate0.988

Unit-step transient response

The curve shows overshoot, damping decay, and the selected settling band.

underdamped, Ts = 1.09 s

Response+/- 2.0% bandDecay envelope

Damping regime

underdamped

damping ratio 0.450

First peak

0.440 s

20.53% overshoot

Decay envelope

3.60 1/s

time constant 0.278 s

Open Source and Easy to Use Elsewhere

This tool is open source and the underlying logic is fully transparent. You can inspect the code, understand the calculations, and contribute improvements. If you want to use the tool in your own website, course page, or learning platform, you can also embed it directly and start from a ready-made iframe setup for this exact tool.

Open source: review the implementation and see how the results are produced.

Embeddable: preview this tool, copy the iframe, and use it in your own site or LMS.