Physics 2210 Preflight 14


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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. A student trying to solve Laplace's equation,
    laplaces eqn
    writes down a trial (separated) function
    trial fn

    For the trial solution that the student has chosen, would k and k' be related to each other, or would they be arbitrary constants? (Choose one)
    Related to each other
    Arbitrary constants (not related to each other)
    Not enough information
    (not answered)

  4. Please explain your answer. If you said k and k' were related, how are they related and how did you decide? If you said they are arbitrary, how did you decide?


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  5. fig3
    Consider two functions of time. Both are small impulses (a square "blip" of length T0, as shown in the figure ), but the first lasts for 1 second, and the second lasts for 2 seconds.
    When you Fourier transform these two f(t)'s you will find the "spectrum" of different frequencies required to build up the impulses.
    Which spectrum will cover a wider range of frequencies?
    You get a wider range of frequencies for the "2 second long" pulse
    You get a wider range of frequencies for the "1 second long" pulse
    Both pulses will have roughly equal ranges of frequencies
    More information is needed (like, which impulse is taller!)
    (not answered)

  6. Briefly, explain your reasoning



  7. 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.




When you are satisfied with your responses click the SUBMIT button.

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