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For Students · Damping Regimes

Damping Regimes for a tele-operated arm

Built for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition. Simulate a tele-operated arm live below — adjust the inputs and watch it respond, right in your browser.

Damping Regimes ComparedLive

under, critical & overdamped

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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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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 students?: Yes — this version of "Damping Regimes for a tele-operated arm" is framed for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.