Physics 2210 Preflight


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The reading assignment for this week would be to finish my lecture notes labeled "PDE", and/or Boas sections 7.12, 13.1 and 13.3

A common physics example involves a square conducting plate, where we solve for temperature T(x,y) everywhere in the plate (satisfying Laplace's equation) subject to some boundary conditions (namely, temperature all around the edges). When you separate variables, T(x,y)=X(x)Y(y), you have to decide whether X(x) will get the "sinusoidal" solution and Y(y) the "exponential", or vice versa.
fig1
  1. For the boundary conditions shown in the figure above, tell us which function, X(x) or Y(y) should get the sinusoidal behavior:
    X(x) is the sinusoidal one here
    Y(y) is the sinusoidal one here
    It makes no difference, you can pick either way.
    Both need to be sinusoidal here.
    Neither should be sinusoidal here (we should use the "separation constant=0" solution)
    More information is needed to decide
    (not answered)

  2. Briefly, explain your reasoning.



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  3. For the boundary conditions shown in the figure above, tell us which function, X(x) or Y(y) should get the sinusoidal behavior:
    X(x) is the sinusoidal one here
    Y(y) is the sinusoidal one here
    It makes no difference, you can pick either way.
    Both need to be sinusoidal here.
    Neither should be sinusoidal here (we should use the "separation constant=0" solution)
    More information is needed to decide
    (not answered)

  4. Briefly, explain your reasoning.

    ____________________________________

  5. Suppose you are told f(x)=A Exp[k x] + B Exp[-k x], where A, B, and k are undetermined constants. What does the boundary condition f(0)=0 tell you? Choose ALL that apply!
    A=0
    B=0
    k=0
    k=n Pi, with n=1, 2, 3, ...
    NONE of these is correct!

  6. Briefly, explain your reasoning.

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  7. Consider two functions of time. Both are small impulses (a square "blip"), but the first lasts for 1 second, and the second lasts for 2 seconds. When you Fourier transform you will find the "spectrum" of different frequencies required to build up the impulse. Which spectrum will cover a wider range of frequencies?
    Wider range of frequencies for the "2 second long" pulse
    Wider range of frequencies for the "1 second long" pulse
    Both will have roughly equal range of frequencies
    More information is needed (like, which impulse is taller!)
    (not answered)

  8. Briefly, explain your reasoning



  9. Please submit a question you have about the reading assigned for the upcoming class. What seemed hard, was something confusing, what would you like us to spend class time on? If you can't come up with any question, how about a comment - (did anything strike you as interesting? )
    Reminder: the reading assignments are on our course calendar


    Thanks for your time.

Optional! - below is a space for any additional relevant comments, thoughts, or suggestions you have.




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