The elastic potential energy of a spring is given by
[tex]E= \frac{1}{2}kx^2 [/tex]
where k is the spring constant and x is the displacement of the spring with respect to its rest position.
Looking at the formula, we can see that E is minimum (zero) when x=0, so when it's at rest position. This means that the elastic potential energy of the system is minimum (zero) when the object is crossing the rest position of the spring.
