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D.E.s and damped systems

  1. Aug 23, 2010 #1
    1. The problem statement, all variables and given/known data

    Let ay'' + by' +cy = R(x)

    Determining whether a system is under/over/critically damped depends on the size of b^2 compared to 4ac.

    Does it depend at all on R(x)?

    2. Relevant equations

    Characteristic equation, quadratic equation.

    3. The attempt at a solution

    I've found a general solution to a D.E. where b^2 < 4ac, and is therefore underdamped (if the D.E = 0)

    However, I'm not sure if I can still conclude that the system is underdamped if the D.E. = R(x).
  2. jcsd
  3. Aug 23, 2010 #2


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    Look after the definition of being under/over/critically damped.

  4. Aug 23, 2010 #3


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    No, it does not. As ehild suggests, surely the definition of "under/over/critically damped" is given in your text?

  5. Aug 23, 2010 #4
    Thanks. The defintion only referred to b^2 - 4ac without explicitly stating that R(x) was irrelevant to damping.
  6. Aug 24, 2010 #5


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