The Student Room Group

SHM in a Potential well

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 ?


ImageUploadedByStudent Room1365065378.289775.jpg
Reply 1
From Hooke's law F = -kx where x is the deviation from the equilibrium. The deviation from the equilibrium in this case is deltax so by comparison k = U''.

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