The period of a pendulum’s swing depends entirely on the length of its string. (Well, the strength of the gravitational field matters too, but that’s more or less the same everywhere on Earth.) This demonstration using a set of fifteen uncoupled simple pendulums of monotonically increasing lengths shows how slight differences in the length of the string translate to differences in the period of the swing and produce a dazzling display of apparent wave behaviour: traveling waves, standing waves, beating, and random motion.
One complete cycle of the dance is 60 seconds. The length of the longest pendulum has been adjusted so that it executes 51 oscillations in 60 seconds, and the length of each successive shorter pendulum is set so that it executes one additional oscillation in this period. Thus, the 15th (shortest) pendulum undergoes 65 oscillations. When all 15 pendulums are started together, they quickly fall out of sync — their relative phases continuously change because of their different periods of oscillation. However, after 60 seconds they will all have executed a whole number of oscillations and be back in sync again.
Find out more at Harvard Science Demonstrations.