Why Pendulum Clocks Synchronize

Why Pendulum Clocks Synchronize
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Hang two pendulum clocks on the same wall, and over time, something strange will happen: the two clocks will tick in synchrony.

Renowned Dutch scientist Christiaan Huygens, the inventor of the pendulum clock, originally noticed this eerie phenomenon back in 1665. Laid up in his bed with an illness, the 36-year-old Huygens found himself entranced by two clocks contained within the same case. No matter how their pendulums were set into motion, within roughly thirty minutes, they would always end up swinging so that when one pendulum reached the apex of its swing the other would reach its apex in the opposite direction. He eventually reasoned that the swings of each pendulum were causing "imperceptible movements" in the beam connecting the two clocks, bringing them into synchrony.

When Huygens shared his observations with the prestigious Royal Society of London, its members were mostly unimpressed. In fact, they took Huygens' observations as a sign that his clocks were fickle, and not as accurate as they were billed to be. 

Experiments carried out nearly 350 years later showed that Huygens was mostly correct in his explanation. When Georgia Tech physicists recreated his clock apparatus, they found that the pendulums exerted miniscule forces on each other through the connecting beam, eventually nudging both into synchrony. The below video shows an approximation of the effect with metronomes.

The flimsy apparatus shown above was designed to exacerbate the effect. So what will happen if two pendulum clocks are connected to a sturdier wall? Turns out, they'll still synchronize, but likely on account of a more subtle form of energy: sound.

Scientists Henrique Oliveira and Luís Melo developed a mathematical model for how two pendulum clocks could affect each other by transmitting a pulse of sound energy once per cycle. They then attached two pendulum clocks to a sturdy aluminum base in close proximity and tested their model by observing the clocks' behavior. As it turned out, the clocks did indeed move into periodic synchrony in a way that remarkably matched Oliveira and Melo's predictions.

The scientists also noticed that external noises, from doors closing to the sound of an elevator, could easily unsettle the system. So if you want to try this it home, keep your voice down!

Source: Oliveira, H. M. and Melo, L. V. Huygens synchronization of two clocks. Sci. Rep. 5, 11548; doi: 10.1038/srep11548 (2015).

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