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For Researchers · Second-Order Step Response

Second-Order Step Response for a CNC toolpath

Built for researchers prototyping or validating an idea. Prototype fast, reproduce exactly, and share a citable, interactive version of your model. Simulate a CNC toolpath live below — adjust the inputs and watch it respond, right in your browser.

Second-Order Step ResponseLive

damping shapes the response

Controls

Presets

Damping ratio ζ

Natural frequency ωₙ

A second-order system's response to a step is set entirely by its damping ratio and natural frequency. Low damping overshoots and rings; ζ = 1 is the fastest response without overshoot; high damping is sluggish. Educational tool.

▶ Run in Python

Data Inspector

Overshoot25%

Settling time (2%)3.33 s

Peak time1.14 s

Regimeunderdamped

Governing equation

y (t) = 1 - e^{- ζ ω_{n} t} (cos ω_{d} t + \frac{ζ}{1 - ζ ^{2}} sin ω_{d} t), ζ = 0.4, ω_{n} = 3

Reading this result: Underdamped: the response overshoots to ~125% of target and rings before settling in about 3.3 s. Lower ζ means bigger overshoot and more oscillation.

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Frequently asked questions

Is this good for researchers?: Yes — this version of "Second-Order Step Response for a CNC toolpath" is framed for researchers prototyping or validating an idea. Prototype fast, reproduce exactly, and share a citable, interactive version of your model.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.