Evolution of The Generalized Coordinates of Pendulum-Spring System

Abstract

The pendulum-spring system studied using Hamilton equations consists of three generalized coordinates. The coordinates are the swing angle of the rod, the swing angle of the spring, and the length extension. In this case, the total Hamiltonian is complicated because of the complicated mechanical system. Six equations of motion are obtained from the Hamilton equations. The visualization of the generalized coordinates with respect to time is illustrated. In the visualization, the spring constant and the initial swing angle of the rod were varied. These variations obtained the harmonic and non-harmonic motion. The motion of such a complex system was usually sensitive to the initial values. Solving the mechanical problems with Hamiltonian formalism could familiarize students with a branch of physics with numerous indispensable applications to other branches.