This study aims to solve a second-order ordinary differential equation that mathematically models the position of a mass attached to a spring over time, with a specific focus on the two-second time interval. This mass-spring system is a physical phenomenon that exhibits behavior closely resembling a sinusoidal wave. This study is conducted within the context of an engineering-oriented differential equations course at a Colombian university using four strategies to accomplish this objective: 1) theoretical modeling, 2) simulated modeling, 3) mathematical modeling by solving a first-order differential equation, and 4) mathematical modeling by solving a second-order differential equation. The analysis of the results will primarily involve comparing the coefficient of determination with the response obtained from the theoretical model. Keywords: numerical differentiation, ordinary differential equations, mathematical modeling, mass-spring system. https://doi.org/10.55463/issn.1674-2974.50.7.14