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Damping and a boiled egg

  1. Feb 20, 2008 #1

    TFM

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

    A hard-boiled egg of mass 51.0kg moves on the end of a spring with force constant 25.7N/m. Its initial displacement is 0.293m. A damping force f (x) = -bv (x) acts on the egg, and the amplitude of the motion decreases to 0.101m in a time of 4.55s.

    Calculate the magnitude of the damping constant .

    2. Relevant equations

    f (x) = -bv (x)

    curly:} w'=sqrt(k/m - b^2/4m^2)

    3. The attempt at a solution

    I used:

    f (x) = -bv (x)

    rearranged to give:

    b = -f/v (x)

    but this didn't work

    Do I have to use:

    curly:} w'=sqrt(k/m - b^2/4m^2)

    and if so, whats the best way to calculate angular frequency (curly:} w')?

    TFM
     
  2. jcsd
  3. Feb 21, 2008 #2

    TFM

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    Any Ideas...?
     
  4. Feb 21, 2008 #3

    HallsofIvy

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    You have "w'=sqrt(k/m - b^2/4m^2)"

    I can assume that m is the mass of 51 kg (are you sure you copied that right?) and b is the damping coefficient you want to find. I can even guess that k is the spring constant 25.7 N/m but unless you tell what w' means, that equation is meaningless.
     
  5. Feb 21, 2008 #4

    TFM

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    It sthe curly Greek w', which I believe means Angular Frequency (?)

    TFM
     
  6. Feb 21, 2008 #5

    TFM

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    Are yes, the egg is 51g:blushing:

    TFM
     
  7. Feb 21, 2008 #6

    TFM

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    I have rearranged the equation to get:

    b^2 = 4m^2*((k/m)-(w'^2))

    I just need to work out angular frequency from the given infomration, but I am not sure what to do...

    TFM
     
  8. Feb 22, 2008 #7

    TFM

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    Any Ideas?

    TFM
     
  9. Feb 23, 2008 #8

    TFM

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    w' is the Greek letter (small) omega with a ' . It says that the angular frequency w' is given by:

    sqrt(k/m - b^2/4m^2)

    But I thought that when a letter has a ' by it, you have to differntiate it?

    Can anyone give me sime ideas about what formula's are suitable to find the angular frequency, given the above initial data?

    TFM
     
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