Abstract:In this report we recall the famous Huygens' experiment which gave the first evidence of the synchronization phenomenon. We consider the synchronization of two clocks which are accurate (show the same time) but have pendulawith different masses. It has been shown 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 pendula in which the phase shift between the displacements of the pendula is respectively close (but not equal) to 0 or π.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 pendula via oscillating beam allowing the pendula's synchronization. Additionally we discuss the synchronization of a number of different pendulum clocks hanging from a horizontal beam which can roll on the parallel surface. It has been shown that after a transient, different types of synchronization between pendula can be observed;(i) the complete synchronization in which all pendula behave identically, (ii) pendula create three or five clusters of synchronized pendula. We derive the equations for the estimation of the phase differences between phase synchronized clusters. The evidence, why other configurations with a different number of clusters are not observed, is given.

In this paper, the phenomena of hysteretic behaviour of friction force observed during experiments are discussed. On the basis of experimental and theoretical analyses, we argue that such behaviour can be considered as a representation of the system dynamics. According to this approach, a classification of friction models, with respect to their sensitivity on the system motion characteristic, is introduced. General friction modelling of the phenomena accompanying dry friction and a simple yet effective approach to capture the hysteretic effect are proposed. Finally, the experimental results are compared with the numerical simulations for the proposed friction model.

No abstract