# Damped Harmonic Motion (Physics)

• November 5th 2009, 08:04 PM
PatrickFoster
Damped Harmonic Motion (Physics)
This is a physics related question involving some calculus.

Quote:

A vertical spring of spring constant 160 http://session.masteringphysics.com/render?units=N%2Fm supports a mass of 80 http://session.masteringphysics.com/render?units=g. The mass oscillates in a tube of liquid. If the mass is initially given an amplitude of 5.5 http://session.masteringphysics.com/render?units=cm, the mass is observed to have an amplitude of 2.4 http://session.masteringphysics.com/render?units=cm after 3.8 http://session.masteringphysics.com/render?units=s. Estimate the damping constant http://session.masteringphysics.com/render?tex=b. 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:

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

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

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

Thanks,
Patrick
• November 5th 2009, 08:54 PM
xxlvh
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?
• November 6th 2009, 01:56 PM
PatrickFoster
Thanks, I was able to solve the problem.