Lissajous Figures - Sand Pendulum

Purpose

To demonstrate Lissajous figures.◙

Equipment

Pendulum on heavy stand, platform and black paper, fine sand.◙

Setup Time

10 min.

Images

g1-71

Description

The bob is filled with sand, displaced from equilibrium and released or gently pushed. Its bifilar suspension causes it to execute Lissajous figures, which are traced out by the released sand.◙

References

Luiz Borello, New Method for Demonstrating the Addition of the Isochronous and Perpendicular Vibratory Motions, AJP 15,◙93-94, (1947). ◙R. H. Romer, A Double Pendulum "Art Machine," AJP 38, 1116-1121 (1970). ◙Chris Chiaverina, A Laser Spirograph for Under $3, TPT 28, 606 (1990). ◙Robert J. Whitaker, A note on the Blackburn pendulum, AJP 59, 330-333 (1991). ◙K. David Pinkerton, Laser Light Fantastic Lissajous Figures, TPT 29, 168-169 (1991). ◙O. Herrera, Mechanical Device to Draw Lissajous Figures, TPT 29, 284-285 (1991). ◙Thomas B. Greenslade, Jr., All about Lissajous Figures, TPT 31, 364-370