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Equation of motion

  1. Dec 3, 2005 #1
    Please , I need to set up the equation for two springs.

    The first one is attached to a ceiling and has a constant k. The second one is attached at the tail of the first one and has a spring constant k'.

    If a mass m is attached to the second spring, How can I set up the equation for the system?
  2. jcsd
  3. Dec 3, 2005 #2


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    the bob will be pulled downward by Earth's gravity.
    It will accelerate downward until the Tension in spring #2 is equal to mg .
    How far has the bob moved by now? What is the effective "k"?
  4. Dec 3, 2005 #3
    well I see what you mean but I dont know the answer.

    I think that the bob will move down by mg=-kx----> x=mg/k''
    k'' is the new constant that I don't know ...

    please help me because I don't understand how the system reatcs...

  5. Dec 3, 2005 #4
    Firstly, you should solve the whole system's K .
    Briefly, F1 is the first spring's force;
    F2 is the second spring's force;
    then you get F1 = k*Deta X1
    F2 = k'*Deta X2
    but if the two springs connected, the force will be the same.
    so k*Deta X1 = k'*Deta X2 = F
    and Deta X = Deta X1 + Deta X2 = F/k+ F/k' = F(k+k')/kk'
    so F=Deta X * kk'/(k+k')
    and mX'' = (X-X0) * kk'/(k+k')
    and you got it.
    good luck :smile:
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