Two Masses connected by Spring, Falling

[plin]

Hi, perhaps a similar thread already exists, but I was not able to find it...

Homework Statement

Two masses m_1 and m_2 are connected by a spring with spring constant D. This setup is attached to the ceiling by a rope. We cut the rope. What happens?

Homework Equations

The center of mass is given by z0 = (z1*m1 + z2 * m2) / (m1 + m2)
The acceleration right after cutting the rope of the upper mass m1 is given by
a1 = (1 + m2/m1)*g
And the acceleration of m2:
a2 = 0
How are the equations of motion in our center of mass system?

The Attempt at a Solution

Find the equations of motion.
Find the frequency of harmonic oscillation.

 

[BigJDubs]

The equations of motion can be derived from Newton's second law: F=ma. For the center of mass, the equation of motion is given by F = m_z0 * a_z0 where m_z0 = m1 + m2 and a_z0 = (1 + m2/m1)*g This equation can be solved using standard techniques to get the equation of motion in terms of the displacement z0: z0(t) = A*cos(wt) where A = (1 + m2/m1)*g/w2 and w = sqrt(D/m_z0). The frequency of harmonic oscillation is given by w = sqrt(D/m_z0).