811 Lissajous Figures in the Sand

First, take note that while the pendulum is capable of oscillating in two directions, the pendulum lengths in the two directions are slightly different.

Picture1

If the periods of oscillation for both modes were exactly the same, the pendulum would be drawing the same straight line in the direction diagonal to the two modes of oscillation, which would be kind of boring. But because the periods of oscillation in the two directions are slightly different, oscillation in one direction always completes just a little earlier than oscillation in the other direction. As result, the pendulum ends up drawing ellipses that spin in then clockwise direction, then anti-clockwise, and so on.

What makes the pattern even more interesting is the fact the osccilations do decay as time progresses due to damping. As a result, the ellipses shrink towards the centre as time progresses.

See also the pendulum in fast motion.

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