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Boundary conditions and Fourier superposition

Keywords: Oscillations & Waves, Superposition, Boundary Conditions, Fourier Series, Small Group Activity


Highlights of the activity

  1. This small group activity is designed to help upper-division undergraduate students learn to apply spatial and temporal boundary conditions to the general form of a Fourier expansion.
  2. Students apply boundary conditions to determine which harmonics are present in a given waveform and observe how that waveform develops in time.
  3. The whole class discussion focuses on applying boundary conditions and the general mechanics of Fourier decomposition.

Reasons to spend class time on the activity

  • An earlier activity discussed initial conditions in time. Here students apply spatial boundary conditions.
  • Students need lots of practice with deconstructing wave forms using Fourier series.
  • In this exercise, they find the components that make a particular 2-component waveform, and animate the superposition to see how the wave form travels.


Instructor's Guide

Student Handouts



Authors: Janet Tate
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