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Relating force constant and frequency to mass

  1. Sep 11, 2007 #1
    1. The problem statement, all variables and given/known data

    A body of unknown mass is attached to an ideal spring with force constant 123 N/m. It is found to vibrate with a frequency of 5.65 Hz.

    Find the mass of the object.


    2. Relevant equations

    F=-kx
    F=ma
    No idea what else...

    3. The attempt at a solution

    No idea where to start. I get to:

    ma=-kx
    m = (-123x) / (a)

    and can't think where to go from there. I've tried:

    1cycle=4 max displacments (x), so
    f=5.65Hz = 22.6 cycles of x /s

    thereby returning x as .25, but that's dead wrong. Any ideas? I'm totally lost.
     
    Last edited: Sep 11, 2007
  2. jcsd
  3. Sep 11, 2007 #2

    andrevdh

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    The mass executes simple harmonic motion. In the relevant theory you can find a relation between the period of oscillations, the mass of the object and the force contant.
     
  4. Sep 11, 2007 #3
    Alright, I got it.

    T = 2(pi)*sqrt(m/k)

    m = k * (T/(2(pi)))^2 = 9.76E-2

    Just for curiosity's sake, was there any other way to do it, that wasn't much harder?
     
  5. Sep 12, 2007 #4

    andrevdh

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    That's the only way I know of.
     
  6. Sep 14, 2007 #5

    dynamicsolo

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    If you're in a calculus-based course, you might be expected to know *how* to get from the force equation F = ma = -kx to the result for the period. But, in the end, you would still apply the period formula you used here.
     
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