# Damped oscillations in a vacuum chamber

Gold Member

## 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

$$0.60=e^{-bt/2m}$$

$$ln(0.60)=-bt/2m$$

$$\frac{b=-(2m)ln(0.60)}{t}=\frac{(-2)(.200)ln(0.60)}{50}=.00409$$

$$0.30=e^{-bt/2m}$$

$$ln(0.30)=-bt/2m$$

$$t=\frac{-(2m)ln(0.30)}{b}=\frac{-(2)(.200)ln(0.30)}{.00409}=118s$$

118s is not correct. Where am I going wrong? This seems like such an easy/straightforward question.

## Answers and Replies

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

ehild

Gold Member
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):

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

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