Synchronization of spring pendula

In this paper, we uncover the phenomenon of synchronization of coupled spring pendula. The model is based on two self-excited nodes with varying lengths (elastic elements), suspended on the horizontally oscillating support. We determine the regions of appearance of synchronous states, describing the co-existence scenarios between possible behaviors. The typical examples of solutions are presented and explained, showing different relations between the pendula and the springs oscillations. The properties of synchronous configurations are examined, including the influence of both the characteristics of the elastic elements as well as the damping within the system. The coherent dynamics is compared with desynchronization, showing that both types of responses can co-exist in various scenarios. The results included in this paper uncover new ways of synchronization of mechanical oscillators and contribute to a better understanding of complex dynamical systems in general.