Math
Sand Lissajous Pendulum
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A pendulum swinging in two directions at once traces a looping curve in a bed of sand, and the exact shape it draws depends on the ratio between its two swing frequencies.
At the Science Playground, swing the pendulum and watch one pattern trace out from start to finish.
Additional Information
These looping curves are called Lissajous figures, named after 19th-century physicist Jules Lissajous, who studied them using vibrating mirrors.
A 1:1 frequency ratio traces a simple circle or ellipse; more complex ratios like 3:2 trace loopier, more intricate patterns.
The same curves show up on oscilloscopes when two sound waves of different pitches are compared against each other.