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

Confederate History - Dispelling the Myths
2015-07-03 3:28
History books, the media, the school systems, etc abound in falsehoods and inaccuracies of Confederate and Southern history. This fact sheet will help to clarify and dispell some of these rampant inaccuracies. MYTH - The War of 1861 - 1865 was fought over slavery. FACT - Terribly untrue. The North fought the war over money. Plain ...
Gays Rights May Open Door for Pedophile Rights
2015-07-03 3:31
Democrats have attempted to normalize pedophilia as a sexual orientation. A recent Supreme Court ruling on same-sex marriage may soon allow pedophiles to argue they are suffering discrimination. “Using the same tactics used by ‘gay’ rights activists, pedophiles have begun to seek similar status arguing their desire for children is a sexual orientation no different than heterosexual or homosexuals,” writes Jack Minor ...
Government Trolls Are Using ‘Psychology-Based Influence Techniques’ On YouTube, Facebook And Twitter
2015-07-03 3:56
Have you ever come across someone on the Internet that you suspected was a paid government troll? Well, there is a very good chance that you were not imagining things. Thanks to Edward Snowden, we now have solid proof that paid government trolls are using “psychology-based influence techniques” on social media websites such as YouTube, Facebook and Twitter. ...
Artificial Intelligence Takes the Battlefield: Who Is Really Running Jade Helm 15?
2015-07-03 2:31
Who is really going to be running Jade Helm 15? There is more to the story than just training for martial law in states designated as “hostile states” – already a chilling pretext with overtones of greater federal power that could spiral out of control. But it seems that it is actually A.I. – artificial intelligence – that is at the helm ...
Robot kills man at Volkswagen plant in Germany
2015-07-03 2:32
A 22-year-old worker was grabbed by the robot and crushed against a metal plate A robot has killed a man at a Volkswagen car factory in Germany. The 22-year-old worker died from injuries he sustained when he was trapped by a robotic arm and crushed against a metal plate. The man, who has not been named, was part of a team that ...
More News »