Lissajous figures

(physics) The path of a particle moving in a plane when the components of its position along two perpendicular axes each undergo simple harmonic motions and the ratio of their frequencies is a rational number. Also known as Bowditch curve.

Plane curves traced by a point which executes two independent harmonic motions in perpendicular directions, the frequencies of the motion being in the ratio of two integers. Such figures are widely used in frequency and phase measurements (see illustration). See also Harmonic motion.

Typical Lissajous figures for ratios of vertical frequency to horizontal frequency. (a) 2:1, with various phase relations. (b) 8:1. (c) 5:4. (After F. E. Terman, Radio Engineers' Handbook, McGraw-Hill, 1943)

The cathode-ray oscilloscope furnishes the most important and practical means for the generation of the figures. The x-deflection plates of the tube are supplied with one alternating voltage, and the y-deflection plates with another. If the frequencies are incommensurable, the figure is not a closed curve and, except for very low frequencies, will appear as a patch of light because of the persistence of the screen. On the other hand, if the frequencies are commensurable, the figure is closed and strictly periodic; it is a true Lissajous figure, stationary on the screen and, if the persistence is sufficient, visible continuously as a complete pattern. See also Frequency measurement; Oscilloscope; Phase-angle measurement.