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!
Munich Jews battle in court over Holocaust remembrance 2015-11-30 20:42
Two Jewish groups in Munich are at odds over how to remember the Holocaust. The situation has escalated, and now one of the groups is suing the city. The argument centers on â€˜Stolpersteineâ€™ - bronze memorial plaques that can be found all over Germany, but not in Munich.
In July, Munich voted to continue the ban on Stolpersteine first introduced in ...
The Pilgrims Were Definitely Not Like Modern-Day Refugees 2015-11-27 20:01
This upcoming Thanksgiving Day is sure to offer you and your family plenty of opportunities to argue over whether America should be welcoming Syrian refugees.
If you have any liberal relatives or friends coming over for your Thursday feast, theyâ€™re going to relish the chance to tell everyone that the Pilgrims were refugees too â€” and hope that statement decimates all ...
ISIS to France: "We will be coming. Victory has been promised to us by Allah" 2015-11-26 3:33
Homegrown French ISIS fighters have issued a chilling threat of new attacks on France just 24 hours after the terrorist group used movie footage of the Eiffel Tower's collapse in another video.
A balaclava-clad militant is seen warning 'we will be coming, we will come to crush your country' in footage posted on Twitter earlier today.
It is unclear where the film ...
ISIS teenage 'poster girl' Samra Kesinovic 'beaten to death' as she tried to flee the group 2015-11-26 1:07 She appeared in social media images for the group carrying a Kalashnikov and surrounded by armed men
A teenage girl who ran away from her Vienna home to join Isis in Syria has reportedly been beaten to death by the group after trying to escape.
Samra Kesinovic, 17, travelled to Syria last year with her friend Sabina Selimovic, 15.
The two became a ...
The Right Stuff's flagship podcast "The Daily Shoah" has been censored by Soundcloud 2015-11-25 22:56
Editor's note: The PC corporate moral police strike again. Just as Radio 3Fourteen & Red Ice Radio were censored from iTunes, The Daily Shoah was pulled from Soundcloud today. As per usual, there is a double standard, they allow any kind of anti-White material:
No counter culture humor making fun of the genocidal mainstream garbage is allowed!
Soundcloud took it upon ...