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Homework Help: Solving for time with an Overdamped Oscillator

  1. Jan 27, 2013 #1
    1. The problem statement, all variables and given/known data
    How long will it take until the mass is within 10% of its equilibrium?

    I already solved most of what is needed in previous parts of the question. I just need help solving for t because it is in two exponents in the equation.

    2. Relevant equations
    This is the equation
    x(t) = A1*e-(γ-q)*t + A2*e-(γ+q)*t
    A1 = 3.61
    A2 = -0.61
    γ = 0.9
    q = 0.64

    3. The attempt at a solution
    First I found where x is .1 from its equilibrium
    x = .1A = .1(3m) = 0.3m
    Then I plugged in the A values. I divided the right side of the equation by x and moved the whole A2 term to the left of the equation to have an exponential on both sides.
    Then I took the ln of both terms to have an equation with t on both sides.
    -(γ+q)*(A2/x )*t = -(γ-q)*(A1/x)*t

    If I plug these variables in, I am left with
    number*t = number*t and that isn't really solvable....
  2. jcsd
  3. Jan 27, 2013 #2
    Everytime I come up with an answer, it is negative but time can't be..
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