We say that the mass comes to rest if, after a certain time, the position of the mass remains within an arbitrary small distance from the equilibrium position. Will the mass ever come to rest

No, the mass will never come to rest

Explanation:

It is so because even at arbitrarily small distance it will experience some amount of force (irrespective of how small the value of force is).

This does not allow the mass to become stationary or in a equilibrium state as it is still subject to some amount of force.

Hence, the the mass will never come to rest

distance = 150m

displ = root (50 ^2 + 100^2)

root(2500+10000)

root 125000