Aspring is stretched from x=0 to x=d, where x=0 is the equilibrium position of the spring. it is then compressed from x=0 to x=−d. what can be said about the energy required to stretch or compress the spring?

The energy stored in the later case is equal to the energy stored in the former  case of the spring.

Explanation:

For a spring we have the expression of kinetic energy as:

where:

k= elastic constant of the spring

x= length of deflection of the spring from the mean position

Here we are given two cases:

CASE:1

x=d

CASE:2

x=-d

So, we get

Just the difference in the two cases is that there is deflection of the spring in the opposite direction.