title: The sympathy of two pendulum clocks: beyond Huygens' observations.
abstract: This paper introduces a modern version of the classical Huygens' experiment on synchronization of pendulum clocks. The version presented here consists of two monumental pendulum clocks--ad hoc designed and fabricated--which are coupled through a wooden structure. It is demonstrated that the coupled clocks exhibit 'sympathetic' motion, i.e. the pendula of the clocks oscillate in consonance and in the same direction. Interestingly, when the clocks are synchronized, the common oscillation frequency decreases, i.e. the clocks become slow and inaccurate. In order to rigorously explain these findings, a mathematical model for the coupled clocks is obtained by using well-established physical and mechanical laws and likewise, a theoretical analysis is conducted. Ultimately, the sympathy of two monumental pendulum clocks, interacting via a flexible coupling structure, is experimentally, numerically, and analytically demonstrated.
authors.affiliation: Center for Scientific Research and Higher Education at Ensenada (CICESE), C.P. 22860, Ensenada, B.C., México.
authors.forename: Jonatan
authors.initials: J
authors.lastname: Peña Ramirez
authors.affiliation: Relojes Centenario, Department of Production Engineering, C.P. 73310, Zacatlan, Puebla, México.
authors.forename: Luis Alberto
authors.initials: LA
authors.lastname: Olvera
authors.affiliation: Eindhoven University of Technology, Department of Mechanical Engineering, P.O. Box 513, Eindhoven, The Netherlands.
authors.forename: Henk
authors.initials: H
authors.lastname: Nijmeijer
authors.affiliation: Center for Scientific Research and Higher Education at Ensenada (CICESE), C.P. 22860, Ensenada, B.C., México.
authors.forename: Joaquin
authors.initials: J
authors.lastname: Alvarez