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Two spring system

  1. Nov 29, 2008 #1
    1. The problem statement, all variables and given/known data
    Consider a system consisting of two springs suspended from the ceiling. The first has a spring constant k-1, the second k-2. They are connected by a mass m and the second spring also has a mass m connected at the bottom. A periodic force is applied to the upper mass. What is the steady state motion for each mass?

    2. Relevant equations
    x1 = Acos wt
    x2 = Bcos wt

    3. The attempt at a solution
  2. jcsd
  3. Nov 30, 2008 #2


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    Welcome to PF!

    Hi mwkfun! Welcome to PF! :wink:

    Show us what you've tried, and where you're stuck, and then we'll know how to help. :smile:
  4. Nov 30, 2008 #3
    I tried two different ways...I attempted to turn the system into an electrical circuit equivalent and I tried with free body diagrams and the following equations:
    mX=mg + k1x1 + k2x2 - Fcoswt
    mX=mg + Fcoswt - k1x1 - k2x2

    (For these two eqns. the X means X double dot indicating acceleration)

    mX2 = mg + k2x2 - Fcoswt
    mX2 = mg + Fcoswt - k2x2

    (again, X2 indicates x double dot...I don't know how to type it the correct way)
    I think I should be solving for x1 and x2, but I am not sure if I have the correct equations. The eqns. reflect the free body diagrams I have drawn. Thanks for any help you can give.
  5. Nov 30, 2008 #4
    I am also wondering whether I should use the x1= Acoswt and x2 = Bcoswt as a substitutions or if they are specific solutions to the differential eqns.
  6. Dec 1, 2008 #5


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    Hi mwkfun! :smile:

    (on this forum, it's best to use dashes instead of dots: X1'' :wink:)

    I don't understand why you've put each of these equations in pairs :confused:

    Anyway, you need to take into account that the displacement of the lower mass is not the same as the displacement of the lower spring … it's the displacement of the lower spring minus the displacement of the upper spring :smile:
  7. Dec 1, 2008 #6
    Thanks so much for your help. I think I got it!
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