Lissajous Figures

Lissajous Figures:

A Lissajous curve (Lissajous figure or Bowditch curve) is the graph of the system of parametric equations which describes complex harmonic motion. This family of curves was investigated by Nathaniel Bowditch in 1815, and later in more detail by Jules Antoine Lissaajous (French) in 1857.

Generation:

Prior to modern computer graphics, Lissajous curves were typically generated using an oscilloscope (as illustrated). Two phase-shifted sinusoid inputs are applied to the oscilloscope in X-Y mode and the phase relationship between the signals is presented as a Lissajous figure. Lissajous curves can also be traced mechanically by means of a harmonograph.

Uses of Lissajous figures:

Lissajous Figures displays the motion of a superposition of two perpendicular harmonic oscillators. The simulation shows the result of the superposition. The amplitude and frequency of the oscillators can be changed. Here are some examples of Lissajous figures.