Amass m is pressed against a horizontal ideal spring with spring constant k. it is not actually attached, so that when the spring is no longer pressing on the mass, the mass separates from the spring.

for parts (a) and (b), assume that the surface on which the mass travels is frictionless.
(a) how far must the spring be compressed for the mass to have a speed v1 when it is at the equilibrium point of the spring?
(b) at what point in the motion does the mass leave the spring (hint: consider the spring force)?

for parts (c) through (d), assume there is a coefficient of friction µk between the block and the surface.
(c) how far must be the spring now be compressed for the mass to have the same velocity v1 when it is at the spring’s equilibrium point? (d) how far beyond the equilibrium point will the mass travel before coming to rest?