Does the Velocity of the Center of Mass Consider the Spring and m2?

[Zamarripa]

Homework Statement

Two masses m1 and m2 are at rest and joined by a spring of length l = 0.5m, as shown in the figure. There is no friction with the surface. In a given moment, an impulse with velocity v0 = 0.2m /s is given to the mass m1 only.

Relevant Equations

Calculate the velocity of the center of mass immediately after m1 has moved
Calculate the position of the center of mass after a time t = 4.0s

I want to know if my solution is correct:

The velocity of the center of mass immidiately after m1 has moved is just
v_cm=m₁v₁ /(m1+m2)

I thing that i have to consider the spring and the m2

 

[haruspex]

The velocity of the center of mass immidiately after m1 has moved is just
vcm=m1v1 /(m1+m2)

Yes.

I thing that i have to consider the spring and the m2

For the second part? Maybe... or perhaps not.