Our demonstration is a copy of one that Bryan Daniels (Ohio Wesleyan University) made for his student research work: which, in turn, appears to be a copy of Pantaleone's model. Thus, in addition to demonstrating the basic physics, this experiment lends itself to modeling diverse phenomena in the life sciences. The phenomenon of spontaneous synchronization is found in circadian rhythms, heart & intestinal muscles, insulin-secreting cells in the pancreas, ambling elephants, drummers drumming, menstrual cycles, and fireflies, among others. Stewart in Scientific American 269(6), 102-109, is a nice biological introduction with more suggested readings. "Coupled Oscillators and Biological Synchronization," by S. Pantaleone provides many excellent references. Phys 70(10), 992-1000, James Pantaleone developed a mathematical model for the metronome system, and discusses how it provides a mechanical realization of the Kuramoto model for synchronization of biological oscillators. In a paper entitled "Synchronization of metronomes," Am. At 176 bpm, they rapidly (within a minute or so) get into sync. The Presto range works well for this particular set-up. The metronomes are Wittner TAKTELL SUPER MINI with a frequency range of 40 to 208 bpm (Largo - Prestissimo). His two pendulum clocks phase locked at 180 degrees (anti-phase). The Interactive Metronome (IM) is a computer-based program designed to improve timing, attention, coordination and regulation in children and adults with a. Apparently Christian Huygens was the first to observe the phenomenon of clock sychronization and inaugurated the study of coupled oscillators. Prof Lars English at Dickinson has experimented along these lines and concluded that it depends on the damping of the base motion-more friction induced the transition (private communication). It certainly appears at the higher frequencies. Occasionally anti-phase locking will happen, but we have not explored under what special conditions this happens. But at least they'd all be playing at the same tempo. If every hippy drum circle had one of these, they'd - well, they'd still be pretty insufferable. Additional parameters that can be varied are (1) the average frequency (bpm), (2) the frequency difference between oscillators (add a dot of modeling clay to the pendulum arm for fine tuning), (3) the base mass, and (4) the damping (maybe put a little oil or other viscous fluid in the aluminum can?). metrognome This is a fine example of gnomish craftsmagnship - it's a little clockwork man that taps a steady, unwavering beat. One can easily change the phase and coupling between the oscillators by simply orienting them at an angle relative to the base board and explore how that affects the system. Having shown this, starting them randomly and then observing them phase lock (when supported by the cans) is even more impressive. As an introduction, it's instructive to demonstrate that the five oscillators (metronomes) are not precisely identical start them together in synchrony on the FoamCore board just sitting on the lecture bench and watch them soon get out of phase with each other, notwithstanding that they are all set to the same number of bpm.
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