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SHM in a potential well

  1. Apr 4, 2013 #1
    In the attachment below some form of link is made between F(x+xo) and dU/dx

    I understand F=-dU/dx but I do not understand the derivation shown to prove that the force constant is equal to the second derivative in the last line.

    How do they go about this proof ?

    ImageUploadedByPhysics Forums1365065923.973605.jpg
  2. jcsd
  3. Apr 4, 2013 #2
    As you saw, if you start with U = 1/2 kx^2 and differentiate once, you get the linear force law you want.
    Differentiate it a second time.
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