Physics art

June 8, 2011 • 1:38 pm

This lovely dance of the pendulums is used as a natural science demonstration at Harvard:

From the Harvard website:

What it shows: Fifteen uncoupled simple pendulums of monotonically increasing lengths dance together to produce visual traveling waves, standing waves, beating, and random motion. One might call this kinetic art and the choreography of the dance of the pendulums is stunning! Aliasing and quantum revival can also be shown.

How it works: The period of one complete cycle of the dance is 60 seconds. The length of the longest pendulum has been adjusted so that it executes 51 oscillations in this 60 second period. The length of each successive shorter pendulum is carefully adjusted so that it executes one additional oscillation in this period. Thus, the 15th pendulum (shortest) undergoes 65 oscillations. When all 15 pendulums are started together, they quickly fall out of sync—their relative phases continuously change because of their different periods of oscillation. However, after 60 seconds they will all have executed an integral number of oscillations and be back in sync again at that instant, ready to repeat the dance.

Setting it up: The pendulum waves are best viewed from above or down the length of the apparatus. Video projection is a must for a large lecture hall audience. You can play the video below to see the apparatus in action. One instance of interest to note is at 30 seconds (halfway through the cycle), when half of the pendulums are at one amplitude maximum and the other half are at the opposite amplitude maximum.

h/t: Matthew Cobb

19 thoughts on “Physics art

  1. Simple and elegant!

    By all rights, that should be accompanied by an audio example of a bunch of different sine waves whose frequencies will drift proportionally and in synchronization with the pendulums. The resultant tones will cause chords to phase in and out of existence and in and out of tune.



    1. It immediately made me think of things I’ve done musically similar to that. Another good musical parallel would be the rhythmicon (search virtual rhythmicon or American mavericks rhythmicon).

  2. That is beautiful. There’s something about oscillations phasing in and out that is quite compelling.

    Here is a performance of the piece “Piano Phase” by Steve Reich, which starts with a 12-note repeating pattern (1 bar of 3/4 time divided into 16th notes) played by two pianos, one of which gradually speeds up until it is one note ahead, then another, and another, and so on. Each time the notes coincide it produces different intervals and the resulting totality is different. Nice piece! (And very difficult to play!)

    1. This put me in mind of Ligeti’s Poème Symphonique for 100 metronomes, though that piece is more concerned with complex emerging patterns from chance rather than simpler juxtapositions as with the Reich (and is also intended to be slightly tongue-in-cheek methinks). Personally I find pieces like the Reich above interesting but, as with other works by him and Glass et al, can’t avoid thinking of them as aural experiments in search of music.

      The Ligeti works quite well visually, at least here anyway – there’s something quite bleak about the blank-faced metronomes ticking away like so many impassive guards, until just one remains.


  3. I think the chronological order of the emergent patterns–double helix, braiding, random motion, illusional beating–runs from 0 to 0:30 and then repeats backwards from 0:30 to 0:60. For example, a few seconds in there is a snake moving away and in the last few seconds a snake moving toward the observer. So cool.

    1. That makes perfect sense–the first second after the pendulums start (each one one second past the coincidence point) is the mirror image of the last second before the pendulums converge again. And the second second maps to the second-to-last, and so on. So there’s a center!

      [I just noticed that my sentence above has both “one one” and “second second” in it. lol.]

  4. The obvious way to design something like that is to first write a computer program to simulate the pendulums on screen, try various values for their periods, observe the results, and then choose the most impressive combination. Then build a real one.

    In fact, I’ll bet that exactly the way it was done.

  5. My undergraduate tutor had something very like this to show us how the ear works by picking up resonant frequencies. The cochlea is basically a rolled up triangular sheet, a lot like the collection of strings in that model. If you hang them on something that will carry the frequency of the swing (like a washing line), and set up another pendulum of a given length a distance away and start that one swinging on it’s own, you find that in your collection of pendulums only the one that’s the same length as the original starts to swing.

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