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Homework Help: Mass Spring Damping Question

  1. May 7, 2014 #1
    1. The problem statement, all variables and given/known data
    Suppose a mass- spring is modeled by x''+ cx'+100x. What should the damping constant c be in order that critical damping occurs?

    2. Relevant equations

    3. The attempt at a solution
    I set the discriminant equal to zero so that there are real repeated roots.
    c=20 or c=-20.
    The answer should only be c=20. For critical damping, the constant must be positive?
  2. jcsd
  3. May 7, 2014 #2


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    What is the repeated root? You need it to be negative so that [itex]x[/itex] decays with time, do you not?
  4. May 7, 2014 #3


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    For any level of damping, c must be positive.

    If c is negative, you are putting energy into the system, not taking energy out.
  5. May 7, 2014 #4


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  6. May 7, 2014 #5


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    An other way to look at it: damping force must be opposite to x', which it is if c is positive:

    x'' = -cx' -100x
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