Why do pendulums synchronise up?

[Eldorado]

The story begins back in 1665, when [Christiaan Huygens] discovered that two pendulum clocks hanging from the same wooden beam would spontaneously synchronise over a period of time. The same principle is then demonstrated with metronomes – an experiment readily recreated in the home.

HackaDay

Huygens’ clocks revisited: Royal Society

20mins:

 

[Grim Reaper 6]

16 minutes ago, Eldorado said:

The story begins back in 1665, when [Christiaan Huygens] discovered that two pendulum clocks hanging from the same wooden beam would spontaneously synchronise over a period of time. The same principle is then demonstrated with metronomes – an experiment readily recreated in the home.

HackaDay

Huygens’ clocks revisited: Royal Society

20mins:

 

Here is a Peer Reviewed Paper that explain why this occurs, below are some paragraphs from the linked paper below

The pendulums synchronise through resonance”. This is not the case. Resonance is just a property of any resonator, whether it is a single pendulum, a balance, tuning fork, quartz crystal, Tacoma Narrows suspension bridge, or organ pipe. Wikipedia says:  “In physics, resonance is the tendency of a system to oscillate with larger amplitude at some frequencies than at others. These are known as the system's resonant frequencies. At these frequencies, even small periodic driving forcescanproducelargeamplitudeoscillations,becausethesystemstoresvibrationalenergy.

Resonancesoccur when a system is able to store and easily transfer energy between two or more different storage modes (such as kinetic energy and potential energy in the case of a pendulum).” Resonance is a property of a single resonator – it isn’t a concept that in itself can explain why two pendulums will synchronise, or for example why they are hard to make synchronise if the coupling isn’t very great. We need to explain what the limits are on synchronisation and how they depend on factors such as the degree of coupling. “

The pendulums correct each other.” I’m not sure what this means. It seems plausible that they might, but what is the mechanism and what are the limits on how much they can be corrected? “Placing a weight to trim the period of one pendulum immediately has the same and immediate effect on the period of the other.” But if you change the rate of one, why do they synchronise at all? And surely changing the natural frequency of one but not the other must introduce some asymmetry into their motions? 

 

Essentially, the reason why a pair of identical coupled pendulums synchronise is this: any even mode oscillation will decay much faster than the odd mode because of increased support loss; only odd-mode energy persists, and so the pendulums apparently synchronise in anti-phase. I say apparently because this is what is observed but the underlying reality is that the other mode is damped out. Often, as in the Breguet and Walter clocks, each pendulum is impulsed by a separate movement.

But as both Bigelow and Gagnier have shown, it is unnecessary to impulse both pendulums – if only one is impulsed and the coupling is high, then both will swing in anti-phase with virtually the same amplitude. 

https://d1wqtxts1xzle7.cloudfront.net/32518209/Asymmetric_coupled_pendulums.pdf?1386653066=&response-content-disposition=inline%3B+filename%3DSynchronous_Oscillations_of_Asymmetric_C.pdf&Expires=1618317562&Signature=ODFdJO43RszULoFtk0ghfnNj-M7FvYvxoqotgIHZD6mrIAe3MUWmPKL~YL1BLiwBv-JoYJ~GtQpK0ChB4YBlqbV2DKXvUfJN5XPezEtlEhZmAke1yfn~lMaL7fF-QD766133DV2Xjf6FwEZd~AtvmoOSPy5uMB71PHw1h6sNKzv-M54THP-bSQ1YZIrGBjB3V4uSaa0EgeETA9hXrjYEFJlndQM1Lbd9XSE8YH2wEa-lPv5s8Qkxo2ncZtKOaLmGCBGm~MUnAM775BQ5CHEt6yeJPOUoTD~9jR9os0gaQUfs04wN01-YPfjNdwxU1-8Ht~4n2JQ6440FXCC~uRmV3w__&Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA

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