NONLINEAR PENDULUM: APPLICATIONS OF DIFFERENTIAL EQUATIONS IN COMPUTER SIMULATION AND SOCIO-ENVIRONMENTAL REFLECTIONS

Abstract

This study uses the mathematical modeling of a pendulum to teach differential equations, combining computer simulation and socio-environmental reflection. Representing a dynamic system that acquires complexity as oscillations increase, the pendulum allows students to explore different behaviors from conservative (linear regime) to chaotic. The qualitative methodology, with participant observation and interviews, uses tools such as the Fast Fourier transform for the purpose of analyzing the nonlinear phenomenon and the Runge-Kutta method for simulating several scenarios (linear/nonlinear), allowing to project the use of the methodology for the purpose of practical and critical analysis of phenomena such as climate change and use of natural resources. Inspired by Critical Mathematics Education (CME), the study seeks to form critical citizens who see mathematics as a tool to interpret and transform reality, in line with the idea of "mathematics in action" defended by Freire and Skovsmose. Thus, it is concluded that the nonlinear pendulum modeling contributes both to the teaching of differential equations and to the development of socio-environmental awareness and education focused on social justice.