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For Engineers · Damping Regimes

Damping Regimes for a balancing bot

Built for engineers using it for real design work. Go from concept to a running model in the browser, then scale to the cloud when needed. Simulate a balancing bot live below — adjust the inputs and watch it respond, right in your browser.

Damping Regimes ComparedLive

under, critical & overdamped

Controls

Presets

Natural frequency ωₙ

Four responses, same natural frequency, different damping. Underdamped overshoots and rings; critically damped (ζ=1) is the fastest with no overshoot; overdamped crawls to target. Most designs aim near ζ=0.7 for a good speed–overshoot balance. Educational tool.

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Data Inspector

ζ = 0.2 overshoot53%

ζ = 0.707 overshoot4%

Critical dampingζ = 1 (fastest, no overshoot)

Governing equation

\overset{x}{¨} + 2 ζ ω_{n} \overset{x}{˙} + ω_{n}^{2} x = ω_{n}^{2} u, ω_{n} = 3.0, M_{p} = e^{- ζ π / 1 - ζ^{2}}

Reading this result: ωₙ = 3: response timescale is about 1/ωₙ ≈ 0.33 s, with the ζ=0.707 curve settling near 1.9 s. Overshoot depends only on ζ, not on ωₙ.

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Frequently asked questions

Is this good for engineers?: Yes — this version of "Damping Regimes for a balancing bot" is framed for engineers using it for real design work. Go from concept to a running model in the browser, then scale to the cloud when needed.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.