This exercise takes the students through the process of discovering how a Gaussian-shaped pulse in a rope can be expressed as the superposition (integral) of sinusoidal waves. It gives practice using the complex form of sinusoidal waveforms, and introduces the Fourier integral as the continuous limit of the Fourier series.

(A quick whiteboard activity is to ask the class to first draw a Gaussian envelope function, then write down the functional form - the first is trivial, the second may take much longer than you think!)

This activity is really a guided lecture, using the notes in the section below. It slows the pace of the lecture, and has the students discussing points in small groups and, in particular, evaluating the integrals needed to give the final form.