Mathematical Modeling Using Second-Order Differential Equations: A Case Study of a Mass-Spring System

José Rodrigo González Granada, Luis Fernando Plaza Gálvez, Eider Leandro Arcila Dager

Abstract

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


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References


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