A device consisting of two coupled pendula, usually oscillating at right angles to each other, which are attached to a pen. The resulting motion can produce beautiful, complicated curves which eventually terminate in a point as the motion of the pendula is damped by friction. In the absence of friction (and for small displacements so that the general pendulum equations of motion become simple harmonic motion), the figures produced by a harmonograph would be Lissajous curves.

# Harmonograph

## See also

Lissajous Curve, Simple Harmonic Motion, Spirograph## Explore with Wolfram|Alpha

## References

Cundy, H. and Rollett, A. "The Harmonograph." §5.5.4 in*Mathematical Models, 3rd ed.*Stradbroke, England: Tarquin Pub., pp. 244-248, 1989.Wells, D.

*The Penguin Dictionary of Curious and Interesting Geometry.*London: Penguin, pp. 92-93, 1991.

## Referenced on Wolfram|Alpha

Harmonograph## Cite this as:

Weisstein, Eric W. "Harmonograph." From
*MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/Harmonograph.html