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Math Help - Damped Harmonic Motion (Physics)

  1. #1
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    Damped Harmonic Motion (Physics)

    This is a physics related question involving some calculus.

    A vertical spring of spring constant 160 supports a mass of 80 . The mass oscillates in a tube of liquid. If the mass is initially given an amplitude of 5.5 , the mass is observed to have an amplitude of 2.4 after 3.8 . Estimate the damping constant . Neglect buoyant forces.
    I have made numerous attempts trying different strategies, but to no avail. I am not sure how to set up this problem. Each time I try to solve for b, I get an equation that is "impossible" to solve (according to Mathematica 7).

    Can someone please explain how to approach this problem?

    Relevant (possibly) equations:

     <br />
x = Ae^{(-b/2m)t}cos\omega't<br />

     <br />
\omega' = \sqrt{\frac{k}{m} - \frac{b^2}{4m^2}}<br />

    m\frac{d^2x}{dt^2} + b\frac{dx}{dt} + kx = 0

    Thanks,
    Patrick
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  2. #2
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    Missing this formula:
    A_2 = A_1^{(\frac{-b}{2m})t}

    0.024 m = 0.055 m^{(\frac{-b}{2(0.080 kg})3.8s}

    Can you work it out from here?
    Last edited by xxlvh; November 5th 2009 at 10:19 PM.
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  3. #3
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    Thanks, I was able to solve the problem.
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