Richard A. Watson on Harmonic Ratios

If you have a pendulum on a string and you have a whole bunch of other pendulums of different lengths that are hanging off a common string, this is called Barton's pendulum.

So if you swing one of those pendulums, it creates a little bit of wobble in the, you know, there's the string that it's swinging on, but then there's the shared string that they're all hanging from.

It creates a little wobble in that shared string.

And that shared string is, you know, just nudging all of the other pendulums which are hanging from it.

Now, if there is another pendulum in that collection, which is the same length as the one that you were originally applying energy to, then the wobble that it receives at the top of the string will resonate with the natural frequency of that pendulum, which means each time it's going this way, it gets a little nudge that goes that way.

And each time it's coming back again, it gets a little nudge that's going back again.

And those energies build up slowly over time.

You know, just like swinging your legs on a swing at the playground, you have to get the swing of your legs in the same tempo as the natural frequency of your pendulum swing on the swing, right? So if the little nudges are the same frequency as the natural frequency of the pendulum, then it picks up, over time, it picks up energy from those little nudges and turns, gets into a larger and larger swing.

So that's a simple example of resonance where two things have the same frequency.

But it turns out that another pendulum that can also pick up energy is a pendulum that is half the length or a pendulum that is twice the length.

And in those cases, it doesn't get a nudge every time it swings, but it gets a nudge every second time it swings.

So it's not going to resonate as strongly.

It only resonates half as strongly if it only gets a nudge every half a time instead of every time.

But it still builds up energy over time.