# Thread: Damped Harmonic Motion (Physics)

1. ## 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:

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

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

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

Thanks,
Patrick

2. Missing this formula:
$\displaystyle A_2 = A_1^{(\frac{-b}{2m})t}$

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

Can you work it out from here?

3. Thanks, I was able to solve the problem.