This is a physics related question involving some calculus.

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).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.

Can someone please explain how to approach this problem?

Relevant (possibly) equations:

$\displaystyle

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

$

$\displaystyle

\omega' = \sqrt{\frac{k}{m} - \frac{b^2}{4m^2}}

$

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

Thanks,

Patrick