Separation of Variables - Cylindrical Coordinates (Part 3)

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Separation of Variables of the Wave Equation on a circular membrane led to a general solution for the vibration of the membrane. It is possible to solve for the arbitrary coefficients by imposing the initial conditions. This leads to the Fourier-Bessel Series.
  1. Dr. Underwood's Physics YouTube Page
  2. Fourier-Bessel Series
  3. Separation of Variables
  4. Wave Equation
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Great videos, well explained and easy to understand - thanks helped me a lot. Is there any chance you might do a video on multipole expansion?

floriank
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Should the substitution in the equation be a Sine and not a Cosine? The Cosine constant sub m, Cm, was determined to be zero. Also, what is title of the continuation of this video?

josechemist
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Can we express any shape of the membrane (that is, any function) by the Bessel-Fourier series?
If that is the case, then why do we need all that fuss with solving the equation anyway? Just use whatever function you want and it will be the solution, right? :|

scitwi