Vibrations of a Circular Membrane With Theta-Dependence

by J. Hebron, SFU, November 1999

This Maple worksheet illustrates the normal modes of oscillation of a circular membrane, including theta-dependence. This problem was solved in the Math 314 Lecture of Monday November 29th, 1999.

In order to get normal modes of oscillation, we choose initial conditions which are described by functions which are already members of the orthogonal set. All the coeffieients in the summation therefore go away except for the term corresponding to the initial condition. Our orthogonal set consists of Bessel functions. We let the radius of the memberae be 1, so becomes , the zeros of the Bessel function.

These animations should be compared to the nodal curves shown in figure 9, page 328 of the textbook.

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Initial condition

Initial condition

Initial condition

Initial condition

Initial condition

Initial condition