Spring mass system?

Question

Two masses M and m are connected by a spring of spring constant k and are placed on a frictionless horizontal surface. Initially the spring is stretched through a distance x when the system is released from rest. Find the distance moved by the two masses before they come to rest.

Answer 1

I will give you a hint in this problem. Hope that someone else is working on this problem to confirm my answer:

1) Force exerted by a spring is given by the Hooke´s Law:

F = -kx
where: F=force
............k = spring constant
............x = distance the spring is elongated

2) As we have the system:

M--cccccccccc---m

3) From the center of the total length of elongated spring, we can compute the force exerted by spring on each mass:

F1 = -kx1 where, x1 = distance thas mass M moves until rest
F2 = -kx2 where, x2 = distance thas mass m moves until rest

4) We solve for x in both cases:

x1 = F1/k
x2 = F2/k

hence: x1 + x2 = (F1 + F2)/k

knowing also that : F = ma.......then:

x1 + x2 = a (M + m) / k

distance moved by the two masses is the sum: x1 + x2

Hope it helps!

Good luck!