Lissajous Figures

Trajectories formed by the composition of two perpendicular simple harmonic oscillations

Tracing Progress: 0%

Frequency A: 3

Frequency B: 2

Phase Delta (δ): 90°

Amplitude A: 200

Amplitude B: 200

Trace Speed: 50

Current Formula:

x = 200 · sin(3t + 90°)
y = 200 · sin(2t)

What are Lissajous Figures?

Lissajous figures are trajectories formed by the composition of two perpendicular simple harmonic oscillations. When a particle participates in two simple harmonic oscillations in different directions simultaneously, its trajectory forms a Lissajous figure.

Applications

Physics Experiments: Used to measure the frequency ratio and phase difference between two harmonic oscillations, observing the composition of two sine signals in oscilloscopes.
Electronic Engineering: Used for signal analysis and frequency measurement in spectrum analyzers and oscilloscopes.
Art and Design: Beautiful symmetrical patterns are often used in artistic creation and decorative design.

Pattern Characteristics

Frequency Ratio Determines Shape: The frequency ratio a:b determines the number of 'lobes' in the horizontal and vertical directions. For example, a=3, b=2 produces a figure with 3 lobes horizontally and 2 lobes vertically.
Phase Difference Affects Pattern: Changing the phase difference δ causes rotation and deformation effects. When δ = 0° or 180°, the figure degenerates into a straight line or simple curve.
Closure Condition: When the frequency ratio is a rational number, the figure is closed; when it's irrational, the figure never closes and gradually fills the entire rectangular region.