Syifa Nurseptiani

Mulawarman University

Zulkarnaen Zulkarnaen

Mulawarman University

Riskan Qadar

Mulawarman University

https://doi.org/10.19184/jpf.v12i4.43632  

ABSTRACT 

Lagrange mechanics is an analytical method in classical mechanics that does not consider forces acting on the system. It focuses instead on kinetic and potential energies as the core of the entire system. The primary goal of this study is to derive the equations of motion for the coupled pendulums connected by a spring system using Lagrange equation. Two identical pendulums, each positioned at the end of its respective lengths, were connected by a spring. Formulating the Lagrangian for this system enabled the derivation of the equation of motion through the Lagrange equation. These equations were graphically represented with predefined initial conditions. The results revealed a recurring pattern: as amplitude of the first pendulum increased, the amplitude of the second pendulum decreased and vice versa. This phenomenon occurs due to the exchange of energy between the two pendulums, where one loses energy while the other gains it.

Keywords: Lagrange equation, coupled pendulums, equation of motion