Homework 9, due December 1, 2004.

[goodwine]

1. Read section 11.5 from the course text.
2. 11.5 number 4. This was done in class, but with a sign error somewhere.
3. 11.5 number 2.
4. 11.5 number 3.

[goodwine]

#3: Section 11.5 gives a solution u(r,t) = sum(c_n*...) (eqn. 21). In the case
of this problem, with u(r,0) = 0, wouldn't this c_n = 0 because it has an f(r)
in the numerator? But since there is an initial velocity should the second
half of the solution presented in class be used (i.e.
sum(sum(J_n()*[c*cos()+d*sin()]*sin() ))? The reason I was wondering is
because this equation involves theta, but in this case u is independent of
theta.

I don't totally follow your question, but this may help.

What the book does is assume that there is no variation in theta, so all the theta stuff goes away. The huge mess of an answer that I gave in class reduces, in that case, to equation (17) which is obviously much simpler. This equation is the starting point for problems 3 and 4. Equation (20) gives the coefficients for the case where there is no initial velocity and a non-zero initial displacement.

When the initial velocity is zero, you are right that c_n = 0, but the purpose of the problem is to work out k_n (not zero). You can do it from the book (you'll have to refer back to one equation from the previous section) or work out how the solution that I gave in class reduces to it (the former is probably easier).

I'm not sure whether or not this helps, but I hope so.

[7]

Any solutions yet?