you use your hand to stretch a spring to a displacement x from its equilibrium position and then slowly bring it back to that position. What is the work done by hand?

Question

you use your hand to stretch a spring to a displacement x from its equilibrium position and then slowly bring it back to that position.  What is the work done by hand?

anonymous · Answer

F=-kx for a spring.
$$W=\int\limits_C \vec{F} \cdot d\vec{r}$$
However, if you move from equilibrium, x=0, to x=x, then back to x=0 then your displacement vector is zero. So I believe the work done should be zero.

anonymous · Answer

$$\int\limits_{x}^{-x}kx dx$$  I beleive malevolence is right, the work will be zero. If you treat the total distance traveled as x.  As the spring is stretched it will travel a distance of x, and as it recoils with the force of the hand still applied it travels a distance of -x.  So the total work done will be  1/2kx^2$$Wnet = 1/2k(-x)^2-1/2k(x)^2 = 0$$