Damped oscillations in a vacuum chamber

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SUMMARY

The discussion centers on calculating the number of oscillations completed by a 200 g oscillator in a vacuum chamber with a frequency of 2.0 Hz, which experiences damped oscillations when air is admitted. The amplitude decreases to 60% in 50 seconds, leading to a calculation error in determining the time when the amplitude reaches 30%. The correct approach involves using the formula for damped oscillations and ultimately reveals that 236 oscillations are completed when the amplitude is 30% of its initial value.

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JJBladester
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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

A=A_0e^{-bt/2m}

The Attempt at a Solution

0.60=e^{-bt/2m}ln(0.60)=-bt/2m\frac{b=-(2m)ln(0.60)}{t}=\frac{(-2)(.200)ln(0.60)}{50}=.004090.30=e^{-bt/2m}ln(0.30)=-bt/2mt=\frac{-(2m)ln(0.30)}{b}=\frac{-(2)(.200)ln(0.30)}{.00409}=118s118s is not correct. Where am I going wrong? This seems like such an easy/straightforward question.
 
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Read the problem carefully, it asks the number of oscillation.

ehild
 
ehild said:
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):

oscillations=(f)(t)=\left (2s^{-1} \right )\left (118s \right )=236
 
Last edited:

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