The potential energy of a particle executing SHM

The potential energy of a particle executing SHM is given by

(a)U(x ) = k(x-a)²/2

(b)U(x)= k1x +k2x²+k3³

(c )U(x) = A e^-bx

(d) U(x) = constant

Ans:(a )

$F -\frac{dU}{dx}$

For$ U(x)= \frac{k}{2}(x-a)^2$

$\frac{dU/}{dx} = k(x-a)$

F= -k(x-a)

This is the condition for SHM about point x= +a
Other functions do not satisfy this condition