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Damped oscillations in a vacuum chamber

  • #1
JJBladester
Gold Member
286
2

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.
 

Answers and Replies

  • #2
ehild
Homework Helper
15,477
1,854
Read the problem carefully, it asks the number of oscillation.

ehild
 
  • #3
JJBladester
Gold Member
286
2
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]
 
Last edited:

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