Modelling a mass-spring system using a second-order homogeneous linear ordinary differential equation with constant coefficients

In this paper, a mass-spring system is considered. The system is modelled using a second-order homogeneous linear (ODE) with constant coefficients. Using this model, the behaviour of the system is studied. The most significant factor, the value of the damping, determines whether the case occurs: no damping, underdamping, critical damping, or overdamping. Each case is mathematically analysed to get parameters that impact how the motion system performs. The obtained solution, which demonstrates the behaviour of the system in a diagram plot of a displacement-time graph and a phase plane graph, is graphically presented in MATLAB software.