The last class I taught was about pendulums, those mundane things that swing back and forth. My favorite illustration of how a pendulum works is the old-fashioned metronome. I still own one like this, somewhere. The lower on the stick you position the weight, the faster the tempo it marks. The one in the picture would be ticking so fast it would be hard to keep up.

This phenomenon illustrates the fundamental principle behind pendulums: that the period of a pendulum (that is, the time it takes for it to swing back and forth) depends on its length, not on the weight or on the angle at which it is released (for small angles). When you move the weight up and down the stick of the metronome, you change the length of the pendulum, and thereby change its period and the tempo it is providing. Nowadays, with metronome apps changing the…