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Homework Help: Proof of stiffness of the horizontal component of a spring

  1. Oct 29, 2013 #1
    1. The problem statement, all variables and given/known data

    Suppose a spring with forces F=k*z. Find the equivalent stiffness of a horizontal spring, where the spring and its horizontal equivalent is seperated by theta degrees. The horizontal equivalent presumably will have a force F(x)=k(x)*x

    2. Relevant equations

    F = F(x)*cos(theta)
    x = z*cos(theta)

    3. The attempt at a solution

    I have try to substitute F=k*z, F = F(x)*cos(theta) and x=z*cos(theta) into the equation F(x)=k(x)*x, but i only end up with a equation k = k(x)*cos^2(theta). The answer should be k(x)=k*cos^2(theta) and it only makes sense if the horizontal equivalent of stiffness is smaller than k. Please help and point out where I have made a mistake. thanks :)
  2. jcsd
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