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For Researchers · Lissajous Curves

Lissajous Curves for a numerical integral

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

Lissajous CurvesLive

harmonic motion in two axes

Controls

Speed1×

Combine two perpendicular sine waves. The frequency ratio a:b sets the number of lobes; the phase δ morphs the shape — the patterns you see on an oscilloscope.

Presets

Frequency a (x)

Frequency b (y)

Phase δ (×π)

▶ Run in Python

Data Inspector

Ratio3:2

Phase0.50π

Closedrational

Governing equation

x = A sin (3 t + 0.50 π), y = B sin (2 t), 3 : 2

Reading this result: Reduced to 3:2, the curve closes into a stable 3-by-2 lobe figure; because the ratio is a whole-number fraction it never drifts, and the phase δ only morphs and rotates that fixed pattern.

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Frequently asked questions

Is this good for researchers?: Yes — this version of "Lissajous Curves for a numerical integral" 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.