Pendulum Waves - Simple Harmonic (and non-harmonic) Motion
2012-01-06 0:00

From: sciencedemonstrations.fas.harvard.edu



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!

From: sciencedemonstrations.fas.harvard.edu



Related Articles
Forgotten In Time: The Ancient Solfeggio Frequencies
The new shape of music: Music has its own geometry, researchers find


Latest News from our Front Page

Why a Caucasian-Japanese is not Percieved as Japanese
2015-08-04 2:15
The Japan Times has a hilarious article about a White guy who is angry and upset at the horrible and racist world we live in because customs agents and border agents are questioning his "right to be Japanese." It's seems that Debito Arodou's experience at border crossings suggest that no one takes a White guy seriously, for claiming to be Japanese. Hmm, ...
"Open the border - we're going to the UK!" Chanting mob of 200 storm Eurotunnel
2015-08-04 1:25
Migrants make their way towards the Tunnel entrance in the early hours of Sunday morning An organised mob of 200 migrants charged into the Calais entrance of the Channel Tunnel early yesterday, chanting ‘open the borders’ and demanding to be allowed into Britain. They tore down fences and charged past police, who retaliated by spraying tear gas. When the migrants were finally ...
Forgotten British Heroes Campaign
2015-08-04 0:16
The text of the letter from the Forgotten British Heroes Campaign to the Israel ambassador in London, Daniel Taub. This will be delivered to the Israel Embassy on Saturday 1st August, the day on which the Campaign will hold a wreath-laying and then a meeting at the site of a notorious Zionist terrorist bombing near to Trafalgar Square (the former British ...
Baltimore Murders Tie Records After Freddie Gray Killing, 45 Killed In July To Make It The Deadliest Month In At Least 45 Years
2015-08-03 23:14
The number of people murdered in Baltimore hit a record-tying 45 homicides for the month of July, the Baltimore Sun is reporting. The number is an uptick that follows a trend of increased violence in the city in the months after the Baltimore riots that resulted from the death of unarmed black man Freddie Gray on April 12. The increased violence in Baltimore, which was already one ...
Executive arrested over disappearance of $390 million in Bitcoins
2015-08-03 23:38
Mark Karpeles, head of collapsed MTGox Bitcoin exchange held by Japanese police Japanese police on Saturday arrested Mark Karpeles, head of the collapsed MtGox Bitcoin exchange, over the disappearance of about $390 (£250 million) worth of the virtual currency, local media said. France-born Karpeles, 30, is suspected of having accessed the exchange's computer system and falsifying data on its outstanding balance, ...
More News »