The potential energy of a particle $\left(U_x\right)$ executing $S.H.M$. is given by
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(a)
$P.E.$ of body in S.H.M. at an instant, $U =\frac{1}{2} m \omega^2 y ^2=\frac{1}{2} ky ^2$
If the displacement, $y=(a-x)$ then
$U =\frac{1}{2} k ( a - x )^2=\frac{1}{2} k ( x - a )^2$
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