Tag Archives: impedance

Pendulums [3] – Coupled Pendulums

Pendulum Week heats up with… coupled pendulums:

(First embed, doubtless of many to come, from the prolific Brady Haran at Nottingham.)

Look in any of those interminable/popular[delete as applicable] ‘Exciting Fun Science Things to Do on a Rainy Day! Science!‘ books and you’ll likely find this old standby, more commonly done with potatoes rather than creme eggs.

It’s not one of my favourites, partly because I think it needs careful performance to appear as amazing as is usually claimed, but also because the subtlety of explanation required hardly seems worth the effort. This film, for example, doesn’t tell us very much. The explanation bit goes:

“There are little forces as [the connecting string] goes out of line that pull from one to the other, transferring energy from [the first pendulum] … over to that one, and then back again.”

Hmm. All that’s doing is describing what we see and replacing the word ‘swing’ with ‘energy,’ and I’m not a big fan of using ‘energy’ as an arm-wave explanation. Robert Winston’s book, snarkily linked above, explains pendulum movement in terms of gravity and momentum, then adds:

“If two pendulums are attached to the same piece of string, they pass their motion back and forth between each other. One pendulum swings, pulling the string it’s hanging from to and fro. This transfers energy to the second pendulum, which starts swinging itself.”

…which, again, is a reasonable description. Is it an explanation, though? I’m unconvinced.

Neither of these ‘explanations’ has begun to cover why it matters that the pendulums are the same length, let alone pesky details like: the demo still works if the connecting string is perfectly taut, when the driving force is delivered by torsion at the suspension point rather than lateral displacement.

But when you try to write a more satisfying explanation you end up in a bit of a mess. I know I did when I wrote this demo into a children’s TV series back in about 1998. A satisfactory explanation has to include (or at least skirt around) energy exchange, mechanical impedance, and resonant frequency – the sheer amount of physics required is, to my mind, beyond what the demo itself will support.

Better, I think, is this variation:

…which is much more clearly about resonance. The inverted spring pendulums also break the visual connection with the phase demonstration in the previous post in this series, which I think would reduce the risk of confusion were one to attempt linking several of these demos together.