How Many Oscillations to Reduce Amplitude by 1000 in a Damped System?

[frostking]

Homework Statement

A mass spring system has the following parameters: damping constant is 1.00 Ns/m spring constant is 1.00N/m and mass is 1.00 kg The mass is displaced from equilibrium and released. Through what minimum number of oscillations must the mass move in order to reduce the initial amplitude by a factor of 1000 or more?

Homework Equations

x(t) = A e ^(-bt/2m) angular accel W = (k/m - b^2/4m^2)^(1/2) T = 2pi/w

The Attempt at a Solution

I computed w and got 0.86 I know that e ^(-bt/2m) is equal to or less than 1/1000 But this is where I get stuck. Some number times w needs to be less than 1/1000 the original amplitude but...I cannot see how to get there. I know from the solution sheet that the answer is two but can someone please show me how to get there? Thanks, Frostking

 

[Delphi51]

frostking, I'm the retired high school teacher here to give a helping hand when I can. It looks like you've got an exponential that needs to be inverted into a log. When you have e^x = .001, you can take the natural log of both sides to get x = ln(.001). I hope that will be useful!