This paper introduces a modern version of the classical Huygens’ experiment on synchronization of pendulum clocks. The version presented here consists of two monumental pendulum clocks—ad hoc designed and fabricated—which are coupled through a wooden structure. It is demonstrated that the coupled clocks exhibit ‘sympathetic’ motion, i.e. the pendula of the clocks oscillate in consonance and in the same direction. Interestingly, when the clocks are synchronized, the common oscillation frequency decreases, i.e. the clocks become slow and inaccurate. In order to rigorously explain these findings, a mathematical model for the coupled clocks is obtained by using well-established physical and mechanical laws and likewise, a theoretical analysis is conducted. Ultimately, the sympathy of two monumental pendulum clocks, interacting via a flexible coupling structure, is experimentally, numerically, and analytically demonstrated.
In this paper, the occurrence of synchronization in pairs of weakly nonlinear self-sustained oscillators that interact via Huygens' coupling, i.e., a suspended rigid bar, is treated. In the analysis, a generalized version of the classical Huygens' experiment of synchronization of two coupled pendulum clocks is considered, in which the clocks are replaced by arbitrary self-sustained oscillators. Sufficient conditions for the existence and stability of synchronous solutions in the coupled system are derived by using the Poincar e method. The obtained results are supported by computer simulations and experiments conducted on a dedicated experimental platform. It is demonstrated that the mass of the coupling bar is an important parameter with respect to the limit synchronous behaviour in the oscillators. Probably, the earliest writing on inanimate synchronization is due to the Dutch scientist Christiaan Huygens (1629-1695), who discovered that two pendulum clocks hanging from a common support show synchronized behaviour. Since then, Huygens' synchronization has drawn the attention of many researchers. 3,7,20,21,28,33 However, a complete understanding of this phenomenon is still missing. Consequently, the present contribution aims to provide new insights into the intriguing synchronization phenomenon discovered by Huygens. In particular, the following questions are addressed: given the Huygens system of coupled pendulum clocks, is it possible to replace the pendulum clocks by other types of second order nonlinear oscillators and still to observe the synchronized motion? Additionally, which is/are the key parameter(s) in the coupled system for the occurrence of in-phase, respectively, anti-phase, synchronization? These questions are answered by means of theoretical analysis, computer simulations, and experiments.
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