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Homework Help: Question on springs

  1. Jan 19, 2010 #1
    Finding the given spring constant

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

    Consider the system represented on the figure, constituted by the mass m and two springs of constant k1 and k2.
    (The image is attached)
    Prove that:

    [tex]\frac{1}{K_{eff}} = \frac{1}{k_{1}} + \frac{1}{k_{2}}[/tex]

    2. Relevant equations

    [tex]F = -kx [/tex]

    3. The attempt at a solution

    I dont know where to begin. I have to consider two different displacements: One for the first spring, and one for the second.
    I think, but I am not sure, that I can consider both forces are equal.

    [tex] F1 = -k_{1} x_{1} [/tex]

    [tex] F2 = -k_{2} x_{2} [/tex]



    [tex] F1 + F2 = 0 [/tex]

    and a resultant force =

    [tex] F_{r} = -k_{eff} x [/tex]


    [tex] x = x1 + x2 [/tex]

    I tried making a system with equations 2 and 1, but I am getting nowhere. Can anyone help?

    Attached Files:

    Last edited: Jan 19, 2010
  2. jcsd
  3. Jan 19, 2010 #2


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    The force on both springs are equal i.e. F1=F2

    Now the force on one spring is also equal to keff(x1+x2).

    I think you can now find keff
  4. Jan 19, 2010 #3
    can you explain why is that so, please?
  5. Jan 19, 2010 #4


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    The force on the spring should be the same throughout.
  6. Jan 19, 2010 #5
    Like this i found it easy to do, thanks.

    but isnt that the force for both springs combined?
    I mean, you have the total displacement, and the Keff.

    Or I can choose any of the springs, say F1 = Keff(x1+x2) ?
    Last edited: Jan 19, 2010
  7. Jan 19, 2010 #6


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    You can choose any spring and it should work out.
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