Huygens' synchronization experiment revisited: Luck or skill?

TL;DR

This study revisits Huygens' synchronization experiment with modern methods, showing that deliberate frequency mismatch increases the likelihood of anti-phase synchronization, suggesting Huygens may have intentionally introduced such mismatch.

Contribution

The paper demonstrates experimentally and numerically that frequency mismatch enhances anti-phase synchronization, providing new insights into Huygens' original observations.

Findings

Frequency mismatch increases anti-phase synchronization probability.

Beyond a critical mismatch, synchronization states abruptly disappear.

Friction and precision influence the critical mismatch value.

Abstract

353 years ago, in a letter to the Royal Society of London, Christiaan Huygens described "an odd kind of sympathy" between two pendulums mounted side by side on a wooden beam, which inspired the modern studies of synchronization in coupled nonlinear oscillators. Despite the blooming of synchronization study in a variety of disciplines, the original phenomenon described by Huygens remains a puzzle to researchers. Here, by placing two mechanical metronomes on top of a freely moving plastic board, we revisit the synchronization experiment conducted by Huygens. Experimental results show that by introducing a small mismatch to the natural frequencies of the metronomes, the probability for generating the anti-phase synchronization (APS) state, i.e., the "odd sympathy" described by Huygens, can be clearly increased. By numerical simulations of the system dynamics, we conduct a detailed analysis on the influence of frequency mismatch on APS. It is found that as the frequency mismatch increases from $0$, the attracting basin of APS is gradually enlarged and, in the meantime, the basin of in-phase synchronization (IPS) is reduced. However, as the frequency mismatch exceeds some critical value, both the basins of APS and IPS are suddenly disappeared, resulting in the desynchronization states. The impacts of friction coefficient and synchronization precision on APS are also studied, and it is found that with the increases of the friction coefficient and the precision requirement of APS, the critical frequency mismatch for desynchronization will be decreased. Our study indicates that, instead of luck, Huygens might have introduced, deliberately and elaborately, a small frequency mismatch to the pendulums in his experiment for generating the "odd sympathy".