Synchronization of two couple pendula in absence of escapement

TL;DR

This paper investigates how two coupled pendula on a movable support synchronize their oscillations without the need for escapement, analyzing the physical parameters influencing this behavior.

Contribution

It models the synchronization process of two pendula on a moving support without escapement, highlighting the parameter conditions that promote synchronization.

Findings

Synchronization occurs under specific parameter conditions.

The model identifies key physical parameters influencing synchronization.

Absence of escapement does not prevent synchronization.

Abstract

A model of two oscillating pendula placed on a mobile support is studied. Once an overall scheme of equations, under general assumptions, is formulated via the Lagrangian equations of motion, the specific case of absence of escapement is examined. The mechanical models consists of two coupled pendula both oscillating on a moving board attached to a spring. The final result performs a selection among the peculiar parameters of the physical process (lenghts, ratio of masses, friction and damping coefficients, stiffness of the spring) which provide a tendency to synchronization.