Simple Harmonic Question

[saltrock]

A mass is attached on a spring .When it is stretched and is let free to move then it oscillates.show that this motion is simple harmomic>>>spring obeys Hook's law.
My workings:
As the mass pulls the spring down mg>-kx but when it as it goes further more down -kx is greater than mg and the apring goes up n hence oscillates.
when the mass goes downwards ,displacement is negative,on the extremevelocity is 0 which means acceleration is maxium.so acceleration is proportional to displacement but due to the negative sign of displacement they are in opposite direction
>>> i am a bit confused how acceleration is in opposite direction to the displacement...My working is a bit mixed up :rolleyes: ..can you give me some better way of answering this question.
Thanks a lot in advance. :smile:

[Borxter]

The spring+mass system will reach an equilibrium where the retarding force of the spring will balance out the gravity. ie mg = kx. This new x will be the position of the new equilibrium. If you now stretch the spring any more, it will behave just like any other spring and obey hooke's law and begin oscillating.