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.
Comments: Our apparatus was built from a design published by Richard Berg 1 at the University of Maryland. He claims their version is copied from one at Moscow State University. Dr. Jiri Drabek at Palacky University in the Czech Republic has informed us that it was originally designed and constructed by Ernst Mach, professor of mathematics in Praha and Vienna around the year 1867. The demonstration is used in the Czech Republic under the name "Machuv vinostroj" -- the "Wavemachine of Mach." The apparatus we have was designed and built by Nils Sorensen.
James Flaten and Kevin Parendo2 have mathematically modeled the collective motions of the pendula with a continuous function. The function does not cycle in time and they show that the various patterns arise from aliasing of this function—the patterns are a manifestation of spatial aliasing (as opposed to temporal). Indeed, if you’ve ever used a digital scope to observe a sinusoidal signal, you have probably seen some of these patterns on the screen when the time scale was not set appropriately.
Here at Harvard, Prof Eric Heller has suggested that the demonstration could be used to simulate quantum revival. So here you have quantum revival versus classical periodicity!
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The City of Casey council now looks likely to withhold planning approval for the development in a special meeting set for Tuesday night.
A council report, to be considered by councillors on Tuesday, recommends that the approval be blocked.
The mosque opponents’ cause has been helped by councillor ...
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Duckenfield told the fresh inquests he had been a Freemason since 1975 and became head of his ...
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Government officials said their city was ‘too multicultural’ to celebrate St George’s Day, England’s version of the 4th of July.
The council said that displaying the English flag may have been seen as “racist” towards immigrants.
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Half of Western European men are descended from one Bronze Age ‘king’ who sired a dynasty of elite nobles which spread throughout Europe, a new study has shown.
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"Local Residents" Are Filmed Stealing Dozens of Bottles of Water at London Marathon Stop 2016-04-25 23:10
Editor's Comment: "Local" residents? Why bother blurring their faces? We know who they are.
London marathon runners were robbed of dozens of bottled waters when thieves raided a refreshment area armed with trolleys during today's race.
Nearby residents - including parents with children - were captured on camera piling up crates of free water handed out by volunteers during the 26-mile event.