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Temporal Analysis of Synchronizing Coupled Pendulums based on Varying String Lengths
  • Niyathi Kukkapalli
Niyathi Kukkapalli
Charter School of Wilmington

Corresponding Author:[email protected]

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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.