Homework 9

[goodwine]

Reading: Chapter 11, sections 1 and 2.

Exercises: here. In addition to the problems indicated on the PDF document, also plot your Fourier series for various numbers of terms. Also plot your solutions to the wave equation for different times to determine the nature of how the solution is changing in time. Include these plots on your homework. Include also a printout of your code that made them, but if the code is repetitive for different problems, it's ok to just submit one and say the other plots were generated by a very similar program.

[kboyle5]

For Problem 2 part a, L is listed as L=10 but the function u(x,0) goes from 0 to 20 and b_n, which depends on u(x,0) has limits of integration from 0 to L. If this L is used the entire range of u(x,0) will not be taken into account. Is there a typo in the question or an I looking at the problem wrong?

[psteven4]

On Problem 1 part b why is the equation f(x=f(x+2)? Since the graphs of the two functions are the same for x=[0,1) and x=[1,2), can't we say f(x)=f(x+1), T=1, and L=1/2? Is there a reason it prompts us with f(x)=f(x+2)?

[ldillon1]

are we supposed to plot only the wave equation at different t for Problem 2?

[goodwine]

On Problem 1 part b why is the equation f(x=f(x+2)? Since the graphs of the two functions are the same for x=[0,1) and x=[1,2), can't we say f(x)=f(x+1), T=1, and L=1/2? Is there a reason it prompts us with f(x)=f(x+2)?

Either way would work.

[goodwine]

are we supposed to plot only the wave equation at different t for Problem 2?

Yes. Problem 1 doesn't have different t (or maybe I am misunderstanding your question).

[matthewpolicelli]

I sent an email about this, but I'll post it here:

For plotting problem 2, how small of a dt should we use? Should there be a clutter of lines, or only 2 or 3, when we plot it?

[goodwine]

I sent an email about this, but I'll post it here:

For plotting problem 2, how small of a dt should we use? Should there be a clutter of lines, or only 2 or 3, when we plot it?

Choose dt such that your plots clearly communicate the nature of how the string is vibrating.