Student handout: Guess the Fourier Series from a Graph

Oscillations and Waves 2023
The students are shown the graph of a function that is a superposition of three harmonic functions and asked to guess the harmonic terms of the Fourier series. Students then use prewritten Sage code to verify the coefficients from their guess. The program allows the students to enter functions of their own choice as well as the one that is preset.
  • Go to Fourier Basis Functions and play with the simulation near the top of the page.
    1. What function does \(a_m\) correspond to? What does \(m\) mean?
    2. What function does \(b_m\) correspond to? What does \(m\) mean?
    3. What values can \(m\) take?
  • Go to Fourier Series: Exploration and look at the simulation near the top of the page. It shows the graph of a function in blue.
    1. Move the sliders until the green curve matches the blue one. Only three of the sliders need to be set to nonzero values.
    2. Based on the graph, why might you anticipate which values of \(a_m\) and \(b_m\) are nonzero, larger or smaller, positive or negative?
Author Information
Corinne
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