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Oscillations Problem: Please help

  1. Nov 21, 2007 #1
    [SOLVED] Oscillations Problem: Please help

    1. The problem statement, all variables and given/known data

    A 290 g air-track glider is attached to a spring with spring constant 4.10 N/m . The damping constant due to air resistance is 2.40×10^−2 kg/s. The glider is pulled out 28.0 cm from equilibrium and released.

    How many oscillations will it make during the time in which the amplitude decays to e^-1 of its initial value?


    2. Relevant equations

    [tex]\omega=[/tex]2[tex]\pi[/tex]/T
    T=2[tex]\pi[/tex][tex]\sqrt{m/k}[/tex]
    Damping: x(t) = Ae[tex]^{-bt/2m}[/tex]cos([tex]\omega[/tex]t)

    3. The attempt at a solution

    I dont even know how to start this

    Thanks so much!!
     
  2. jcsd
  3. Nov 21, 2007 #2

    G01

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    Well, we know the damping coefficient, b, correct? Can you use this to find the time it takes for the oscillation to decay the specified amount?
     
    Last edited: Nov 21, 2007
  4. Nov 21, 2007 #3
    is t= m/b?
     
  5. Nov 21, 2007 #4

    G01

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    Your a little off. Consider this:

    The amplitude of the wave at any time t is given by:

    [tex]Ae^{-bt/2m}[/tex]

    The initial value is A, so we want to know the time that:

    [tex]Ae^{-bt/2m}=Ae^{-1}[/tex]

    What does this equation give you for the time?
     
  6. Nov 21, 2007 #5
    Um i got 24.2
     
  7. Nov 21, 2007 #6

    G01

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    Sounds good to me. Now can you take this time value and use it to find out how many oscillations the system undergoes in that time? HINT: You'll need the period. How can you find that from the known information?
     
  8. Nov 21, 2007 #7
    from Period= 2pi(m/k)^.5

    but i dont see where the period comes in
     
  9. Nov 21, 2007 #8

    G01

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    Oops! I meant to say the frequency, sorry! The frequency gives you the number of oscillations in one second, correct? So, using that, how many oscillations in 24.2 seconds?
     
  10. Nov 21, 2007 #9
    Im completely lost now
     
  11. Nov 21, 2007 #10

    G01

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    You want to know how many oscillations happen in 24.2 seconds, correct?

    Well,

    the # of oscillations in one second = frequency

    So if you know the frequency, you know the number of oscillations in one second. Using that information, it is a basic math problem to find the number of oscillations in 24.2 seconds. You know how to do this part if your this far into a physics course. Think about it.
     
  12. Nov 21, 2007 #11
    got it thanks so much!!!
     
  13. Nov 21, 2007 #12

    G01

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    Good Job!
     
  14. Nov 21, 2007 #13
    Wow, someday I will be able to do that lol. GO1 recommend any sources for physics tutorials or something?
     
  15. Nov 22, 2007 #14

    G01

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    The one that is always recommended around here is hyperphysics:

    http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html

    This is a good tutorial and it is trustworthy and accurate.

    If this doesn't satisfy your curiosity then I would suggest investing in a textbook. Good luck!
     
  16. Nov 22, 2007 #15
    Thanks. Really interesting stuff, really like the website. What text would you recommend for a beginner, I am taking physics now but its easy. Lately we have studied frictional forces such as F=un and F=ma, but this is over my head. Go1 what degree do you have?
     
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