Homework 10

[goodwine]

Reading: All of chapter 11.

Note: change k=4 pi^2 to k = 9 pi^2 for problem 1.

Exercises: here (updated to final version 12:35pm, Friday).

Notes: 1.1 you only have to do it for a couple intervals. If you do several you will see a pattern, but it's only required to do the first two intervals.

1.2 using ode45() is fine. Make sure to run the program long enough to understand the true nature of the way the mass is moving. This will be helpful for you in solving 1.3.

2. Plug and chug.

3. The eigenvalue is lambda. You need to show that the BC can't be satisfied unless lambda has the right sign.

4. Follow the derivation for Laplace's equation in the book. The non-zero BC is on a different edge, though, so that will make you work through the whole process.

5. This is actually pretty easy, but you need to go through the steps to derive the equation.

6. You have to work through the whole thing from the beginning: assume u(x,t) = X(x) T(t) ...

[jmcgill1]

On problem 1, I'm getting a problem when trying to graph the solution since there are multiple (4pi^2 - (npi)^2) terms in the denominators of my solution, the solution is undefined when n = 2. Is there a way to avoid this?

[goodwine]

On problem 1, I'm getting a problem when trying to graph the solution since there are multiple (4pi^2 - (npi)^2) terms in the denominators of my solution, the solution is undefined when n = 2. Is there a way to avoid this?

FYou should use 9 pi^2 like I had indicated in my email and this page also says.

The reason it is undefined is that is the resonance frequency of the mass-spring system. You need to take that term out of the series and separately multiply it by t.