Beautiful, out-of-phase pendulums

This Harvard physics apparatus uses a series of pendulums of varying lengths, swinging together, to make a mesmerizing dance:

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.

Our apparatus was built from a design published by Richard Berg [Am J Phys 59(2), 186-187 (1991)] at the University of Maryland. The particular apparatus shown here was built by our own Nils Sorensen.

Pendulum Waves (via Kottke)


    1. Ever created something beautiful, clever, or positive in your life? I leave that for you to think about.

  1. I am reminded of many of the old school Amiga demos… I suspect I’m in the minority, but at the same time I’m sure I’m not the only one on boingboing to think that…

  2. I love how you see progressions from one pattern to the next; it’s as if they are connected in the same way as circles, ellipses, parabola and hyperbola are all just part of the continuum of conic sections.

    1. I don’t know what this UVA Chorus is supposed to be, but I guess the video doesn’t do it justice: it seems utterly devoid of interest, both visually and acoustically.

  3. Nils’ dad was my high-school physics teacher, and always had cool demos. Partly because of him I majored in physics. Good job!

  4. mesmerizing…reminds me of the night i grokked beat frequencies: i was watching tv w/ the sound off (but listening to music;-);-);-) and a commercial shows 2 guys walking along, just their legs, going in & out of sync: aHa! i saw the beat!

  5. Now, can people please stop asking why we find science, physics, and engineering to be such interesting topics? Try it, you’ll see the beauty in it.

  6. Here’s an interesting question that has nothing to do with physics for all the language nerds out there:

    Why is ‘pendulums’ not ‘pendula’ as in ‘bacteriums’ are ‘bacteria’?

    1. Why is ‘pendulums’ not ‘pendula’ as in ‘bacteriums’ are ‘bacteria’?

      There are plenty of such conundra.

      Old gag for UK-ian speakers:
      “Have you concluded your experiments with the pendula?”
      “Yes, sir, we’re sitting on our ba doing our sa.”

  7. The obvious sound track would have been György Ligeti’s Poème Symphonique for 100 metronomes (1962).

    @BunnyFooFoo since Ligeti thought of doing this 50 years ago, science is imitating art in this case.

    @Steve. Good question!

    1. I wasn’t familiar with that piece before you mentioned it. But, now that I’ve look at a few minutes, I can’t say that any of the performances that I’ve seen are anything like this video. Mainly for two reasons:
      1) The metronomes never seem to be tuned to a precise number of BPM
      2) They never seem to be started properly in phase, so, even if they were tuned to an exact integer number of BPM, it wouldn’t show the same patterns as you see in this video as the absense of phase synchronization would distort the patterns beyond recognition.

    1. Me, too. In fact, after watching this, I had to dig through my Delicious bookmarks to find it. Looks like I discovered it back in October ’06.

  8. I had to watch it twice – the first time I simply watched the patterns as the progressed from shape to shape, the second time I tried to follow a single pendulum throughout (it’s quite difficult to maintain that focus, at least for me).
    Bizarrely hypnotic and attractive.
    Thanks for posting.

  9. If you relax your eyes it looks like the spears are orbiting in 3d, as if around a single axis, instead of in a line. Starting at about :33, try to see it as a snake coiling around a central point, and it progresses from there. It’s a weird effect, and much more interesting than watching them phase in a line (tho that’s pretty awesome too.)

    Does that work for anyone else, or is it just me?

  10. Chaos and order. The double helix. This video contains an explanation of the universe and the meaning of life.

  11. I’m out the door, headed to the big swingset at the playground. Surely this will scale up. Perhaps I will need to help matters out by putting the a fat kid on one end and a toddler on the other.

  12. What a coincidence. My physics teacher played this video to us today as a sort of introduction to waves.

  13. I think the San Francisco Exploratorium has a gizmo like this, if you want to go stare at one IRL

  14. Does anyone have a vertical (looking down) view of this?

    To me, this looks like the pendulum swings would form a sine wave seen in that plane. The apparently-random view from the end that we see here shows points on a sine wave that is slowing down thereby becoming a lower-frequency wave. We are basically seeing the familiar mathematical graph from the Z axis rather than the usual X-Y planes. A vertical view should be easier to understand – but this is more fun.

  15. How long before some advertising agency uses this in a television commercial. In 3D.

  16. @38 the random pattern is seen because this is a discrete representation of a sinusoid, and its frequency is increasing until it can no longer be correctly “sampled” as a sinusoid by the relatively low number of pendulums/discrete timepoints (low sampling resolution) after it gets around 3x starting frequency. As the frequency increases, it occasionally reveals harmonics in odd/nth points, until it hits the nyquist frequency and reflects, then decreasing all the way down to zero, before staring up again.

    Extended to many more periods’ worth of pendulums, and redesigned to allow for consistent raising/lowering of the strings with barrel cams, this would make an excellent visual exhibition of frequency modulation & modulation index.

  17. I wonder what the minimum number of pendulums for this to work would be… and how slow they could go…

  18. I build toys (volunteer) for the Science Playground (ages 2-6) at OMSI.
    Does anyone have plans for this? I think the kids would love it.

  19. I am 62 years old and I finally understand what the term physics means! Such order and beauty and I’ve missed it most of my life. Thank you all for the comments. I’ve had a fascinating morning following your leads and learning and being centered in my awe.

  20. As I look at the beauty of this display of simple harmonics of physics, it reminds me of the ordered world we all live in. It is part of what brought me to be an engineer, as well as what brought me to remain in respecful awe of the Creator of such a universe! Thank you for this wonderful exhibit.

  21. I found this most challenging. Has anyone described an equation that defines this motion?

    Bob Franklin

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