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

Huygens' synchronization experiment revisited: Luck or skill?