10178

# Generating Lissajous Figures

Given two wheels connected by a belt and a point on the outer rim of each, one can generate a Lissajous figure by the motion of the wheels. The coordinates of a point on a wheel can be described by sine functions of a certain frequency and phase shift. The ratio of the radii at the ends of the belt determines the relative frequencies of the coordinate of the red point on the upper left wheel and the coordinate of the red point on the lower right wheel. If the starting position of a point on a wheel is offset by a certain angle, a phase shift occurs in the sine functions describing the coordinates of the point.
Drag either red point to move both wheels and the curve will be traced. You can change the radius of the axle on the lower right wheel and the offset angle between the starting positions of the points with the sliders. The radius controls the relative frequency of the and coordinates. When it is a rational number, a closed curve is generated; when it is irrational, the curve never closes and fills the square. The offset angle determines the phase shift of the coordinate of the red point of the upper left wheel and affects the shape of the Lissajous figure generated.

### PERMANENT CITATION

Contributed by: Michael Rogers (Oxford College/Emory University)
 Share: Embed Interactive Demonstration New! Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details » Download Demonstration as CDF » Download Author Code »(preview ») Files require Wolfram CDF Player or Mathematica.

#### Related Topics

 RELATED RESOURCES
 The #1 tool for creating Demonstrations and anything technical. Explore anything with the first computational knowledge engine. The web's most extensive mathematics resource. An app for every course—right in the palm of your hand. Read our views on math,science, and technology. The format that makes Demonstrations (and any information) easy to share and interact with. Programs & resources for educators, schools & students. Join the initiative for modernizing math education. Walk through homework problems one step at a time, with hints to help along the way. Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet. Knowledge-based programming for everyone.