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!
Estonia must accept African & Middle Eastern immigrants says politician 2015-05-22 3:06
Kalle Laanet, an Estonian politician, spoke at the International Migration Forum held in Tallinn. He told the audience that the question is not: Should Estonia take the African and the Middle Eastern immigrants (who illegally entered Southern Europe)? He said the question is: How will Estonia take the immigrants?
â€śToday the issue is not whether Estonia should receive the refugees coming to ...
Rescuing Palmyra: History's lesson in how to save artefacts 2015-05-21 22:49
With Islamic State militants now inside the historic town of Palmyra in Syria, the question, inevitably, is whether they will destroy the ancient ruins.
As IS continues to sweep through parts of Iraq and Syria, damage to centuries-old artefacts - because IS sees statues and shrines as idolatrous - is plentiful.
But history has shown that, when culturally important sites are under ...
Saudi Arabia Wants to Convert Sweden to Islam 2015-05-21 20:38
Aje Carlbom is an Associate Professor of Social Anthropology, University of Malmö
Since the 1970s, Saudi Arabia has actively spread its interpretation of Islam, Wahhabism or Salafism, worldwide. It is the most literal version of Islam and affects many young Muslims, who regard society as a place to Islamize, writes social anthropologist Aje Carlbom.
Sweden's Foreign Minister Margot WallstrĂ¶m was ...
Professor: If You Read To Your Kids, You're 'Unfairly Disadvantaging' Others 2015-05-21 18:22
According to a professor at the University of Warwick in England, parents who read to their kids should be thinking about how they're "unfairly disadvantaging other people's children" by doing so.
In an interview with ABC Radio last week, philosopher and professor Adam Swift said that since "bedtime stories activities . . . do indeed foster and produce . . ...
If You Read About Conspiracies You're Just Like Osama Bin Laden Apparently 2015-05-21 3:46
At its heart, the story of Osama bin Laden's time at his house in Abbottabad is surreal. The American image of bin Laden - leering at us from under his head wrap as he plots and schemes - is undermined by the mundane realities of his life. The guy was responsible for murdering thousands of Americans and orchestrating a global ...