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Find potential energy function and show that it is proportional to displacement

  1. Oct 20, 2012 #1
    1. The problem statement, all variables and given/known data
    Find the potential energy function for a spring if the origin is placed at the wall and the unstretched length of the spring is L. Show that with a suitable choice of the constant, this potential function is proportional to the square of the amount that the spring is stretched or compressed.


    2. Relevant equations
    F = d(h(x))/dx (F = force function)
    U(x) = -h(x) (U(x) is potential energy function)


    3. The attempt at a solution

    Force of the spring
    F = -kx

    I integrated F and made the result negative to get the potential energy function
    kx2/2 + C

    But the Textbook solution is:
    kx2/2 - kLx + C

    How do I get -kLx? Also, I'm not sure about how I should start the second part of the problem.
     
  2. jcsd
  3. Oct 20, 2012 #2
    x is the distance from the wall, so the force is -k(x-L).
     
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