As many books,including mine (Principles of Physics by Resnick and Halliday) introduce, I also will present my example like this:
Let there be a spring of negligible mass attached on one side with a wall and free on the other side. A block of $m$ with velocity $v$ hits the free side of the spring, compressing it until its KE is 0. Then the spring will relax again to make the block move until its velocity is $v$.
Now, according to the books:
When the block was compressing, it was doing work against the spring force and its KE was converting to PE. Thus this is a case of conservative force .
Is this so? Really?
Let us think in terms of Newton's third law, and the laws of conservation of momentum and energy.
When the block started to compress the spring, the restoring force was opposing its movement. So, by Newton's third law, the block would impart the same force on the spring on the left. So, the block does work on the spring resulting in decreasing of its kinetic energy. So, wasn't the spring moving? Wouldn't it possess kinetic energy? If so, how should there be potential energy?
And the spring ought to have kinetic energy, otherwise the momentum of the spring-block system wouldn't be conserved. OK, if I say the wall can't be neglected, then if it had moved due to the force by the block, wouldn't the KE of the block go to the KE of the wall and of the moving spring?
So, what is going on? Why does the spring have PE? Isn't the spring moving? Can't these laws be applied here?