Ensino das funções periódicas com experimento prático e aplicação da transformada de Fourier na modelagem de dados no ensino médio-técnico

Abstract

In the search for alternative means for teaching mathematics, modeling persists as one of the most effective actions, with the purpose of modeling real-life situations, obtaining equations that allow simulating certain phenomena. Attributing this ideology to this ideology, this work presents the use of trigonometric functions, more specifically the Fourier transform, through an experiment, to obtain characteristic signals of vibration amplitude in dynamic systems. This is a low-cost experiment, applicable in high school/technical education, through a pedagogical practice. In the search for works focused on teaching periodic functions of the type sense and cosine, a systematic review was carried out, identifying the absence of publications of works that are directly related to periodic functions with the Fourier transform in high school/technical education. However, in the systematic review, a large number of publications of works using the Fourier series and transform in various applications in the branches of science and engineering in solving characteristic problems of signals. The method employed in this work was based on an experiment that uses equipment to generate characteristic vibration signals. Initially, a spreadsheet was used to work with known periodic functions, gradually evolving to the experiment with more specific applications in vibration signals. The study contributes to the pedagogical practice that allows the student to learn periodic functions of the sine and cosine type, initially applying the basic concepts of the functions, which can be compared to real situations with the use of the spreadsheet. The proposed pedagogical practice aims to contribute to the teaching of sine and cosine functions with the application of the practical experiment, allowing the student to identify the use of mathematics in specific or real applications.