Question: A particle oscillates in one dimension about the equilibrium position subject to a force $ F _{xx}(x) $ that has an associated potential energy U(x). If k is the force constant, which one of the following relations is true?
Options:
A) $ F _{x}(x)=kx^{2} $
B) $ F _{x}(x)=kx $
C) $ U(x)=\frac{1}{2}kx $
D) $ U(x)=\frac{1}{2}k^{2}x $
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Answer:
Correct Answer: B