More complicated example

Consider a mass $m$ attached to a spring with spring constant $k$, sitting on a frictionless table at rest. A free mass, also with mass $m$, moves towards the first mass with velocity $v$ and does a head on elastic collision with it.

a

What are the velocities right after the collision?

b

What is the maximum compression of the spring?

c

What is the time the interval between the first collision, and when the masses recollide?

d

What are the final velocities are the masses?