Simple harmonic motion,the restoring force?

[harjyot]

at the extreme position, the restoring force that developed, is it's magnitude more than the initial force imparted? and that's why it goes back to the mean position or is it that, the magnitude is same and it just goes back to attain stable equilibrium?.

 

[mfb]

at the extreme position, the restoring force that developed, is it's magnitude more than the initial force imparted?

Which "initial force imparted"?
It depends on your setup, in particular on your initial force.

 

[harjyot]

the question should be I think,
that how is it that the displacement on either side of the mean position is same?

 

[mfb]

In a symmetric setup (and a harmonic potential is symmetric), it follows from symmetry and energy conservation.

 

[harjyot]

And if we were to understand how the mechanics of it actually works.
can it be that at the initial state, kinetic energy is imparted by a force, now this momentum is opposed by a restoring force which keeps on decreasing the momentum till the body comes to a rest state, here the kinetic energy is completely changed into potential energy, now this restoring force makes the body go to it's mean position, now here again it over shoots because of the momentum and the same cycle is repeated?

 

[Doc Al]

Yes, in simple harmonic motion (with no damping or energy leakage) PE and KE are exchanged as the mass oscillates about the equilibrium point. The total mechanical energy remains constant.