Simulation of Damped Oscillation Decay in a Single-Degree-of-Freedom Mass-Spring System

MATLAB provides an excellent platform for simulating the decay process of a single-degree-of-freedom mass-spring system under damping effects. This simulation employs numerical integration methods like ode45 to solve the second-order differential equation: m*x'' + c*x' + k*x = 0, where m represents mass, c denotes damping coefficient, and k indicates spring stiffness. Through this implementation, we can effectively analyze the dynamic response characteristics of spring oscillators and observe how dampers influence system energy dissipation. The simulation allows parameter adjustment to explore different system responses, including underdamped, critically damped, and overdamped conditions. Key MATLAB functions used include ode solvers for equation integration and plotting functions for visualizing displacement-time relationships. This analysis facilitates comparison between experimental results and theoretical predictions, enhances understanding of the system's physical properties, and establishes a foundation for developing more accurate models of complex systems.