Temporal Analysis of Synchronizing Coupled Pendulums based on Varying
String Lengths
Abstract
Christiaan Huygens, in the 1600s, discovered the synchronization of
coupled pendulums while considering a specific closed system. This paper
furthers Huygensâ\euro™s ambitions by considering the effects of
synchronization time based on changes in string length in coupled simple
pendulums designed on a moving platform. Two simple pendulums were
connected through the medium of a wooden board which was then placed on
cylindrical cans. String length and synchronization time seemed to
display an inverse relationship based on trends of raw data.
Explanations for other behaviors such as brief stops in motion and
anti-phase versus in-phase synchronization are explained using various
laws of Classical Mechanics and are modeled with linear approximations.
The effect of synchronization arises from the medium between the
pendulums and the various dampenings of the system. The findings
presented generally show that synchronization can be optimized which is
useful in various fields of study like the medical field where many
diseases are caused by the synchronization of neurons. Finally, the
equations of motion and energy are modeled with Lagrangian physics and
Mathematica software. Possible extensions, like creating a model similar
to the Kuramoto Model, and other applications of the problem are
discussed.