Lagrangian Equation of Coupled Spring-Pendulum System

A coupled spring-pendulum system in a conservative field was studied where the equation of motion of the system using Lagrangian and Hamiltonian equation were obtained. The equation of motion represented by a second-order differential equation from the three generalized coordinate were used. The potential energy equal to zero when the system is in its equilibrium position. The generalized coordinate that being used were the angle of the first pendulum θ_1, the angle of the second pendulum θ_2, and the increase in the length of the spring x. The resulting equation of motion can be used to determine the dynamics behavior of the system at any time. Students' understanding is expected to be more complete by providing a procedure to derive the Lagrangian equation of motion.