Abstract
We consider the synchronization of two clocks which are accurate (show the same time) but have pendulums with differentmasses.We show that such clocks hanging on the same beam can show the almost complete (in-phase) and almost antiphase synchronizations. By almost complete and almost antiphase synchronization we defined the periodic motion of the pendulums in which the phase shift between the displacements of the pendulums is respectively close (but not equal) to 0° or 180° . We give evidence that almost antiphase synchronization was the phenomenon observed by Huygens in XVII century.We support our numerical studies by considering the energy balance in the system and showing how the energy is transferred between the pendulums via oscillating beam allowing the pendulums’ synchronization.
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Czolczynski, K., Perlikowski, P., Stefanski, A., Kapitaniak, T. (2013). Synchronization of Two Nonidentical Clocks: What Huygens was Able to Observe?. In: Kyamakya, K., Halang, W., Mathis, W., Chedjou, J., Li, Z. (eds) Selected Topics in Nonlinear Dynamics and Theoretical Electrical Engineering. Studies in Computational Intelligence, vol 459. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34560-9_1
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