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I would like to present this as an interesting demonstration of resonance. Resonance, as you may know, is a key concept in the theory of sound and it affects many of the processes we use every day in music production and sound engineering, both live and in the studio.
Please watch the video. You don't need to watch it all, you can skip through it quickly if you like...
I watched this live on TV as part of the Diamond Jubilee concert of June 2012, and I was fully expecting Grace Jones to put down the hula hoop after a few seconds, or certainly by the end of the first verse of her song Slave To The Rhythm. But she kept it up the whole way. Wow, I don't think I could do even a single full turn. Of course, her costume helps. But now the science...
The hula hoop works on the principle of resonance. Put a little bit of energy into the hoop every so often, and the hoop will gyrate easily. Get the timing wrong and the hoop will fall to the ground. And you will look an idiot.
So all Grace has to do, considering that clearly she has had a lot of experience in hula hooping, is give the hoop a little push with her hips every time it goes round, and the hoop will spin with very little effort.
The hoop will only spin at the rate it wants to. The diameter of the hoop dictates its resonant frequency. So a small hoop will want to spin faster than a large one.
So how does Grace manage not only to keep the hoop spinning at the correct rate, and also sing in time with the music? The answer is that the hoop has been selected so that the rate of spin matches the tempo of the song. Clever. Well it almost matches, but the Q factor of the resonance isn't so high that Grace's rhythmic hip movements are too far off the required pace.
OK, so it's a novelty performance. But its an interesting novelty. Whoever thought of the idea perhaps doesn't wholly deserve a knighthood from the Queen, but I'd buy them a drink and hear their story about how it all came together.
By the way, if you want to learn more about the mathematics of the hula hoop, you might start here (if you have time on your hands)...
Coordination Modes in Multi-Segmented Rhythmic Behavior: The Dynamics of Hula Hooping by Ramesh. Balasubramaniam and Michael T. Turvey.
They won a Nobel Prize for that. (Er, actually an Ig Nobel prize.)
P.S. I said that the resonant frequency of the hoop was determined by its diameter. If you read the paper you will see that it's rather more complicated than that :-)