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Maximum Initial Speed of an Overdamped Oscillator

  1. Oct 7, 2012 #1
    1. The problem statement, all variables and given/known data

    An overdamped oscillator with natural frequency w and damping coefficient y starts out at a position xo>0.

    What is the maximum initial speed (directed toward the origin) it can have and not cross the origin?

    2. Relevant equations

    Overdamped Case Equation

    x(t)=Ae^(-(y-ohm)t) + Be^(-(y+ohm)t)

    3. The attempt at a solution

    Differentiating the above equation, simplifying, differentiating again and setting it to 0 and solving to t(max)....but I get stuck here with a really complicated equation.
    I'm not sure how to solve for A and B given the initial condition of xo>0.

    Can someone set me in the right direction?
     
  2. jcsd
  3. Oct 8, 2012 #2
    What you should probably do first is to solve A and B in terms of y, w, x0 and v0. Once you have them, just plug them into the formula for x(t), then find when x(t) = 0 and solve v0 from that.
     
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