Synchronization of Mechanical Oscillators: An Experimental Study

Abstract

In this research we consider synchronization of oscillators. We use mechanical metronomes that are coupled through a mechanical medium. We investigate the problem for three different cases: 1) In passive coupling of two oscillators, the coupling medium is a one degree of freedom passive mechanical basis. The analysis of the system is supported by simulations of the proposed model and experimental results. 2) In another case, the oscillator is forced by an external input while the input is also affected by the oscillator. This feedback loop introduces dynamics to the whole system. For realization, we place the mechanical metronome on a one degree of freedom moving base. The movements of the base are a function of a feedback from the phase of the metronome. We study a family of functions for the reactions of the base and their impact on the behavior of the metronome. 3) We consider two metronomes located on a moving base. In this case the two metronomes oscillate and as the base is not freely moving, they are not directly coupled to each other. Now based on the feedbacks from the vision system, the base moves and hence the phases of the metronomes are affected by these movements. We study the space of possibilities for the movements of the base and consider impacts of the base movement on the synchronization of metronomes. We also show how such a system evolves in time.