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SHM: Mass on a string

  1. Jan 8, 2009 #1
    1. The problem statement, all variables and given/known data

    A 2 kg object hangs from a spring, the mass of which can be discounted. When the object is attached, the spring extends by 2.5cm. The top of the spring is then oscillated up and down in SHM with an amplitude of 1mm. If Q=15 for the system, find w_0 (angular frequency) and the amplitude of the forced oscillation at w=w_0.

    2. Relevant equations

    F=-kx, F=mg
    (w_0)^2=k/m
    x=Acos(w_0*t + phi)
    Q=w_0/gamma, where gamma is the width.

    3. The attempt at a solution

    Setting the gravitational force equal to the restoring force gives mg=-kx, rearranging gives (w_0)^2=k/m=-x/g=(0.025m)(9.81m s^-2)=0.245m^2 s^-2

    Using that value for w_0 and the given one for Q I found gamma to be 0.016. Since this is less that 2w_0, there's heavy damping. Not sure how to progress from there, the fact that amplitude's involved i think i need x=Acos(w_0*t + phi), but how to deal with the time and phase difference? Any push in the right direction would be appreciated.
     
  2. jcsd
  3. Jan 8, 2009 #2
    First: I'm concerned about your units in w_0 (which is supposed to be a radial frequency, therefore it should have unit of radians/sec...)
     
  4. Jan 8, 2009 #3
    I see what you mean, I was just trying to be consistent with the units on the RHS without thinking of the quantity involved.
     
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