As Pendulum Week continues here you’ll have noticed a pattern building up: that pendulums crop up in all sorts of demonstrations, but it’s often rather tricky to pin down satisfying explanations for their behaviour. Pendulums appear simple and straightforward to grasp, which is usually a good sign for demonstration tools as we want audiences to engage with ideas or behaviour and not be distracted by unfamiliar apparatus. However, I wonder if it’s possible that pendulums are too simple, in that their apparent simplicity seems to lull us into forgetting their subtleties.
Heck, unless you’re in that sin θ ≈ θ small-amplitude space you haven’t even, technically, got simple harmonic motion. Most of the time, pendulums don’t even swing like, well, pendulums. Ouch.
It feels like it ought to be possible to link pendulum demonstrations together in a neat story. A mass on the end of a string is about as simple as physics apparatus gets, surely there’s a delightful sequence of demos which can build successively, one on the other, to arrive at something complex and surprising and revealing about the world? That’s got to be possible, right?
Perhaps it is, but the origin of this series of posts lay in my noticing that pendulum demos aren’t alike, and the distinctions seem to me to be of the subtle-and-confusing kind rather than the subtle-but-illuminating kind.
Probably the best attempt I’ve seen to navigate the resulting swamp was by my colleague Marty Jopson, who made this film for the first series of Science Shack (skip to 2:40 for the start of the show):
Marty and I were co-producers on the series, and if I remember correctly he won awards for this show. I wasn’t, I should say, much involved with this episode (harrumph), but it’s still worth a watch. It gets into some of the subtleties about resonance and synchronisation that we’ve seen in this series of posts.
To my mind this demo isn’t an example of resonance… and that’s a thought we’ll pick up in the next post in this series. Meanwhile, please do share your favourite pendulum demos in the comments. Or, you know, any pendulum-related anecdotes – there’ll never be a better time for those.
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.
After the previous post I may have got a little carried away, and we’re declaring this Pendulum Week on ScienceDemo.org. Fresh pendulum action every morning.
This beautiful demo wasn’t something I’d seen before this film appeared, though the Harvard demos folks behind it trace its history to the University of Maryland in the early 90s, and from there back to Moscow State University previously. Everything old is new again.
Anyway, it’s a beautiful demonstration of pendulum periodicity and, through that, phase. Note that the previous pendulum demo was about the efficiency of energy conversion, and hence the only real link between these two demos is the pendulum itself. You may spot a theme developing here.
It’s so well-known it was included in the recent BBC Challenger dramatisation of Feynman’s last great adventure, previously mentioned on this blog, only to my mind the dramatisation did it badly. With a longer pendulum drop the energy loss is minimal, and you really want your back and particularly the back of your head to be braced against a wall, as shown in the film above. If you stand in open space you’re at significant risk of swaying a little, and with a long enough pendulum you may have only millimetres of leeway.
It’s also one of those demos for which I’ve been wary of using volunteers. If they muck around at all they risk a bowling ball to the face, but sometimes a volunteer’s trust that you the performer wouldn’t let any harm come to them is stronger than their understanding of the physics. This is one of those situations where the science is considerably more reliable than the test subject.
Besides, I reckon the best way of performing this demo wouldn’t involve a person at all, but rather a priceless vase borrowed from a museum. Sadly, I’ve never seen it done that way.