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Critically damped oscillations

  1. Jul 7, 2011 #1
    1. The problem statement, all variables and given/known data

    A mass m moves in one dimension x subject to a restoring force −kx and a damping force −γ[(x)\dot]. What are the conditions for underdamped oscillations, overdamped oscillations, and critical damping?
    Now, suppose m is 0.80 kg, γ is 1.18 kg/s, and the oscillations are critically damped. What is k?

    The object starts at rest, displaced by some amount a. At what time is the displacement a/2?

    2. Relevant equations

    [itex]\beta[/itex]=[itex]\gamma[/itex]/(2m)

    3. The attempt at a solution

    Ok so I know k=0.435 N/m

    and I know the solution for the diff eq for critical damping is:

    x(t)=(A+Bt)e^(-[itex]\beta[/itex]t)

    my problem then becomes solving for A and B.
    from the given info I would think x(0)=a and x'(t)=0
    giving me A=a and B=[itex]\beta[/itex]a.

    I am not sure if this because when I solve for t at x(a/2) I do not get the right answer
     
  2. jcsd
  3. Jul 7, 2011 #2

    vela

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    How did you solve for t? I found t=2.28 s.
     
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