# Definition:Lissajous-Bowditch Figure

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## Definition

A **Lissajous-Bowditch figure** is a plane curve which is the locus of a point whose coordinates move in simple harmonic motion.

The specific shape of a **Lissajous-Bowditch figure** depends on the relative frequencies and phases of the two motions.

## Examples

### Example: $\map \cos {4 t + \frac \pi 2}$ by $\map \sin {5 t}$

The Lissajous-Bowditch figure generated by the simple harmonic motions:

\(\ds x\) | \(=\) | \(\ds \map \cos {4 t + \frac \pi 2}\) | ||||||||||||

\(\ds y\) | \(=\) | \(\ds \map \sin {5 t}\) |

is as follows:

## Also known as

A **Lissajous-Bowditch figure** is also known as:

## Also see

- Results about
**Lissajous-Bowditch figures**can be found**here**.

## Source of Name

This entry was named for Jules Antoine Lissajous and Nathaniel Bowditch.

## Sources

- 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**Lissajous figures** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**Lissajous figures**