Lagrangian Equation of Coupled Spring-Pendulum System

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