Lissajou′s Figures

The pattern traced out when the displacements of two simple harmonic motions are traced in the x and y direction. The displacements may be written as:

where

x = displacement on x axis

y = displacement on y axis

A₁, A₂ = amplitudes

ω₁, ω₂ = angular frequency

φ₁, φ₂ = phase

Phase 0° 45° 90° Frequency ratio 1:2 1:3 2:3

See also: Simple Harmonic Motion.