DYNAMICAL MODE OF CASE STUDY ON MASS-SPRING SYSTEM ON A MASSLESS CART: COMPARED ANALYTICAL AND NUMERICAL SOLUTIONS

In this research, we study the dynamical behaviors of a mass-spring system on a massless moving cart. The Lagrangian of the system was first constructed, which resulted in obtaining the Euler-Lagrange equation (ELE) of the system. As a next step, we used the Laplace transformation technique to attain an exact solution for ELE of the system. Furthermore, numerical and simulation techniques were applied with the help of MATLAB software, where we solved ELE numerically for some specified initial conditions. Simulation results indicate that they are in good agreement with the exact analytical solution. Finally, some simulation results were presented in this research.