Damped oscillations in a vacuum chamber

[JJBladester]

Homework Statement

A 200 g oscillator in a vacuum chamber has a frequency of 2.0 Hz. When air is admitted, the oscillation decreases to 60% of its initial amplitude in 50 s.

How many oscillations will have been completed when the amplitude is 30% of its initial value?

Homework Equations

[tex]A=A_0e^{-bt/2m}[/tex]

The Attempt at a Solution

[tex]0.60=e^{-bt/2m}[/tex][tex]ln(0.60)=-bt/2m[/tex][tex]\frac{b=-(2m)ln(0.60)}{t}=\frac{(-2)(.200)ln(0.60)}{50}=.00409[/tex][tex]0.30=e^{-bt/2m}[/tex][tex]ln(0.30)=-bt/2m[/tex][tex]t=\frac{-(2m)ln(0.30)}{b}=\frac{-(2)(.200)ln(0.30)}{.00409}=118s[/tex]118s is not correct. Where am I going wrong? This seems like such an easy/straightforward question.

 

[ehild]

Read the problem carefully, it asks the number of oscillation.

ehild

 

[JJBladester]

Read the problem carefully, it asks the number of oscillations...

I need to slow down sometimes! Thanks for the heads-up. Here is the last step I was missing (and the correct answer):

[tex]oscillations=(f)(t)=\left (2s^{-1} \right )\left (118s \right )=236[/tex]