Solving Question 2: Separation of Variables

[FunkyDwarf]

Homework Statement

Not sure if you guys can get this link
http://www.maths.uwa.edu.au/devsite/Units/math3341-s1-2008-crawley/assignments-solutions/Sheet%204
should be able to.
Question is question two.

Homework Equations

Not many besides the general separation of solutions sort of thing but I am a bit unsure how to apply that with three variables.

The Attempt at a Solution

In previous examples we had some symmetry that meant we could knock out say the theta dependence on something but I am not sure here. I tried letting u = T(t)R(r)K(theta) and just fiddling a bit but came up trumps as i tried to fit the R function to a solution of the bessel function which we expect from what's given. I get the T(t) function as a sin + cos solution with argument lambda*c where -lambda squared is the constant i assign to the two sets of functions in separation of variables. Thats sort of right i guess, not sure where the plus or minus comes from but then again i don't know how they get omega. I think I am on the right track looking for the solution form of u i gave I am just not sure how to follow through nor how to link the two constants that arise from applying separation of variables twice.

Hope that made sense :S
Cheers
-G

EDIT: Nevermind, I am retarded and can't read my own notes/do algebra properly. Mods can delete if you want.

 

[FunkyDwarf]

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