Pendulum Waves

This week’s entry in the “Wow, the Internet is Awesome!” file:

http://www.youtube.com/watch?v=yVkdfJ9PkRQ

These pendula of staggered lengths are set swinging, and the result is fascinating.  At first, the weights seem to trace out sine waves, but they quickly start to cycle through a wide range of behaviors.

At times the pendula appear highly organized, and at times almost chaotic, as they cycle through various patterns.  Amazingly, the weights eventually return to their initial state!

A really beautiful mathematical demonstration.