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


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!


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

The Aeon of Horus is Ending and the Elites are Nervous as their Icons are Dying
2014 04 18
I predict there is going to be a huge resurgence of interest in European indigenous spiritual traditions from Norse to Celtic/Gaelic to Slavic and so on. Millions of Europeans are going to realise that we are the victims of Christianity and New Age garbage. Their bastardised Kabbalah, the psychic force used by Crowley and the elites to cement his Aeon ...
Easter - Christian or Pagan?
2014 04 18
From: Contrary to popular belief, Easter does not represent the "historical" crucifixion and resurrection of Jesus Christ. In reality, the gospel tale reflects the annual "crossification" of the sun through the vernal equinox (Spring), at which time the sun is "resurrected," as the day begins to become longer than the night. Rather than being a "Christian" holiday, Easter celebrations date back ...
Man-Made Blood Might Be Used in Transfusions by 2016
2014 04 18
Researchers in the U.K. have created the first man-made red blood cells of high enough quality to be introduced into the human body The premise of the HBO show and book series True Blood revolves around a technological breakthrough: scientists figure out how to synthesize artificial human blood, which, as an ample new source of non-human food, allows vampires to "come ...
The Trials of the Cherokee Were Reflected In Their Skulls
2014 04 18
Researchers from North Carolina State University and the University of Tennessee have found that environmental stressors – from the Trail of Tears to the Civil War – led to significant changes in the shape of skulls in the eastern and western bands of the Cherokee people. The findings highlight the role of environmental factors in shaping our physical characteristics. ...
Our Fears May Be Shaped by Ancestral Trauma
2014 04 18
Last December, an unsettling Nature Neuroscience study found that mice who were taught to associate the smell of cherry blossoms with pain produced offspring who feared the smell of cherry blossoms, even if they had never been exposed to it before. We knew that the process was epigenetic—that it was not hard-wired in the permanent genetic structure of the mouse—but ...
More News »