## College Physics (7th Edition)

$(x^{2}-x_{0}^{2})$.
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 $(x^{2}-x_{0}^{2})$.