Bill Goodwine's Courses

Reading: Chapter 11, sections 3 and 4.

Exercises: 11.2 (let m=1, b=0 and k = 9 pi^2), 11.4 (number 4 only) and 11.6.

In problem 11.2, do we need the mass "m" to solve the problem?

ccheney wrote:In problem 11.2, do we need the mass "m" to solve the problem?

Yes, sorry about that. I added m=1 to the problem statement.

I'm having trouble with 11.4, number 4. How should we get started on that?

pat wrote:I'm having trouble with 11.4, number 4. How should we get started on that?

I need a more specific question to give a useful answer. Basically it's what I did in class yesterday.

I get the steps we did in class yesterday, but how do we incorporate the initial condition that gives a piecewise du/dt?

pat wrote:I get the steps we did in class yesterday, but how do we incorporate the initial condition that gives a piecewise du/dt?

I don't have the book with me right now. Does it give an initial condition for u or for du/dt? If the former, you just evaluate u(x,0) and use a Fourier series-type computation to find all the coefficients. If it's du/dt and the problem is a heat conduction problem, then that is a mistake. Because it's first-order in time, you only need initial values for u, not derivatives. Please let me know if it says du/dt and is also conduction, because if that's the case I need to clarify it for the whole class.

The problem is for the heat equation, the initial condition for u(x,0) = 0, but then it gives a piecewise initial condition for du/dt(x,0) along the length L. The other problems give a piecewise initial condition for u(x,0) and do not mention du/dt.

pat wrote:The problem is for the heat equation, the initial condition for u(x,0) = 0, but then it gives a piecewise initial condition for du/dt(x,0) along the length L. The other problems give a piecewise initial condition for u(x,0) and do not mention du/dt.

Then that's a typo. The initial conditions should be for u, not du/dt. Just do the problem for the given profile for u instead of the derivative.