This pair of pendulum experiments was acquired from Chamboree 2018 and while they're not related scientifically we haven't figured out what to do with them. The uncoupled pendulums could join 'Welcome to CHaOS' for the briefly chaotic phase and the weakly coupled ones could join 'Resonance' if they work how I think they do.

Uncoupled Pendulums

To set this up you'll need to have two equal sized supports, using a combination of tables and boxes works well. You'll want to view them from above or down the length (e.g. from under the table).

There are several uncoupled simple pendulums of monotonically increasing lengths which dance together to produce visual travelling waves, standing waves, beating, and random motion. One might call this kinetic art and the choreography of the dance of the pendulums is stunning! Aliasing and quantum revival can also be shown.

The period of one complete cycle of the dance is t (60) seconds. The length of the longest pendulum has been adjusted so that it executes some number (51) oscillations in this t (60) second period. The length of each successive shorter pendulum is carefully adjusted so that it executes one (perhaps) additional oscillation in this period. Thus, the 15th shortest pendulum (or however many there are) undergoes 65(ish) 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 t (60) seconds they will all have executed an integral number of oscillations and be back in sync again at that instant, ready to repeat the dance.

One instance of interest to note is at t/2 (30) seconds (halfway through the cycle), when half of the pendulums are at one amplitude maximum and the other half are at the opposite amplitude maximum.

It's worth noting the mass has no effect on the period of the pendulum (however gravity strength does) so it doesn't matter about the number of washers on the strings.

The demonstration is used in the Czech Republic under the name Machuv vlnostroj—the "Wavemachine of Mach." Harvard also have one which is used in one of their museums.

James Flaten and Kevin Parendo have mathematically modelled the collective motions of the pendula with a continuous function. The function does not cycle in time and they show that the various patterns arise from aliasing of this function—the patterns are a manifestation of spatial aliasing (as opposed to temporal). Indeed, if you've ever used a digital scope to observe a sinusoidal signal, you have probably seen some of these patterns on the screen when the time scale was not set appropriately. You could talk about sampling and trying to guess the pattern if you know about this.

You can also talk about Reset times, after t seconds we're back to where we started and the system has reset, this is an important part of Markov chains and other probabilistic results, if the system resets (or regenerates). This means we can treat parts of the process as independant statistically. It could be used to simulate quantum revival. So here you have quantum revival versus classical periodicity! Quantum revival is when we complete a full period of the system wave function, something which often takes a long time.

Coupled Pendulums

You want to hang the sting between two fixed boxes and then try swinging various pendulums, you'll notice as there weekly coupled you can occasionaly get other pendulums to also swing due to them having resonant periods.