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.

9 thoughts on “Pendulums [3] – Coupled Pendulums”

  1. Coupled pendulums are entertaining – I did some swings at Snibston that worked on this principle, I think they’re still there 20 years on. Francis Evans built the inverted spring pendulum thingy to explain why height is not necessarily the main determinant as to how much a building sways in an earthquake too.

  2. I might have known Francis would be involved somewhere, heh. Marty did a lovely demo for Science Shack, back in the day, which illustrated the use of water tanks to damp building oscillations. The uprights for his ‘skyscraper’ used breadsticks, as I recall (or was it linguine?), which were a wonderfully rubbish engineering material but surprisingly consistent in their behaviour.

    I’ll have to try to track that down.

  3. I’m interested in the order these demos are developed. Is it “here’s a cool thing that a pendulum can do, now let’s work out how to describe it simply” or “here’s what we want to say about pendulums, now let’s find a demo to illustrate it”. I’m not sure that both routes can (or should) lead to the same result, but I’m not sure which was the case for the videos above. I think my preference would be for information first (what, how complex, for whom), then pick the demo…

  4. I agree that the linked pendulum “explanation” wasn’t very helpful. Framing things in terms of energy doesn’t add anything.

    At school we did a practical where we measured the period of a mass suspended from a spring, oscillating up and down. The tricky bit about the experiment was that the mass/spring could also swing like a pendulum, and what happened was that the mass alternated between oscillating up/down and swinging side-to-side. The problem was that counting the up/down oscillations was tricky when their amplitude faded to zero every so often!

    It’s all very well talking about the energy passing from one pendulum to another, but in this case, the energy was passing from the mass/spring to…the mass/spring!

  5. A bugbear of mine is calling pushing a kid on a playground swing an example of resonance. It’s true that coinciding your pushes with the natural frequency maximises amplitude, but because it’s just a little ‘impulsive’ push, you could time it any any point when the swing was moving forwards and get the same result (f0 just means you can stand still and push something that’s slowed down).

    Sitting on the next swing along and telling your kid to hold a slinky would be better, and more fun. 🙂

    1. I saw the pendulums the other day and waecthd it twice in a row, drooling from mesmerization.It’s fun to pick one and follow it, which breaks the illusion somewhat, then pull back to see the whole and have it kick back in.I’m gonna watch it again now

  6. Seeing that second video reminded me of a discovery I made with a head massager (see here for an image: ). There is usually two different lengths of ‘arms’. If you flick one of the arms, all the arms of that length start to vibrate whereas the different length ones are stationary and v.v.

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