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Damped oscillator

  1. Mar 11, 2007 #1
    1. The problem statement, all variables and given/known data
    Show that the area in phase space of a cluster of orbits for the damped simple harmonic oscillator given in the lecture varies in time as:
    [tex]A(t) = A(0) e^{(-r/m)t}[/tex]


    2. Relevant equations
    [tex]\dot{x} = (1/m) y[/tex]
    [tex]\dot{y} = -kx - (r/m) y[/tex]

    3. The attempt at a solution
    I don't understand the question. I don't see how an orbit - which is a line - can have an area. I'm guessing that the result is found by some integration of the given equations, but since I don't see how the statement of the question makes any sense, I can't follow the logic.

    Edit: bah. Copied down the wrong equation. The correct one is now quoted. Still, knowing the right one isn't enlightening me on what to do.
     
    Last edited: Mar 11, 2007
  2. jcsd
  3. Mar 12, 2007 #2
    Nobody?

    Is the question nonsense, or have I not explained properly?
     
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