Answer
$(x^{2}-x_{0}^{2})$.
Work Step by Step
Potential energy at position $x_{0}$ = $\frac{1}{2}kx_{0}^{2}$
Potential energy at position $x$ = $\frac{1}{2}kx^{2}$
So, change in potential energy =$\frac{1}{2}k(x^{2}-x_{0}^{2})$.
i.e. proportional to $(x^{2}-x_{0}^{2})$.
