Question

when a spring is released from unstreched position , we have to find its maximum elongation
1. if we equate forces , kx=mg we get x=mg/k
2.if we equate the energy change , we get : 0.5kx^2=mgx
x=2mg/k
how can we get two different answers ?

Answer 1

The first one is correct. In the second one, every part of the spring is not moving by x. Thus, it won't be mgx but mgx/2 considering centre of mass of the spring.

Answer 2

I believe that your notion, kx=mg, is wrong.
But the second one is right.
Anyways, why did you equate the forces? The body is neither at rest nor in uniform velocity. At the extreme point, the particle might be momentarily at rest, but this doesn't imply that its acceleration is nullified.