- #1

kraigandrews

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- 0

## Homework Statement

A mass m moves in one dimension x subject to a restoring force −kx and a damping force −γ[(x)\dot]. What are the conditions for underdamped oscillations, overdamped oscillations, and critical damping?

Now, suppose m is 0.80 kg, γ is 1.18 kg/s, and the oscillations are critically damped. What is k?

The object starts at rest, displaced by some amount a. At what time is the displacement a/2?

## Homework Equations

[itex]\beta[/itex]=[itex]\gamma[/itex]/(2m)

## The Attempt at a Solution

Ok so I know k=0.435 N/m

and I know the solution for the diff eq for critical damping is:

x(t)=(A+Bt)e^(-[itex]\beta[/itex]t)

my problem then becomes solving for A and B.

from the given info I would think x(0)=a and x'(t)=0

giving me A=a and B=[itex]\beta[/itex]a.

I am not sure if this because when I solve for t at x(a/2) I do not get the right answer