What is the Angular Frequency of Two Masses on a Spring?

[americanforest]

Homework Statement

We attach two blocks of masses m1 = 10 kg and m2 = 4 kg to either end of a spring of spring constant k = 4 N/m and set them into oscillation. Calculate the angular frequency ω of the oscillation

Homework Equations

$$M_{1}{x}^{..}=k(w-x)$$
$$M_{2}{w}^{..}=-k(w-x)$$

where x and w are the distance from equilibrium position of m1 and m2 respectively.

Attempt

Honestly, I have absolutely no idea. How does one start this?

 

[Avodyne]

Notice that the right-hand sides depend only on w-x. Wouldn't it be nice if you had an equation where the left-hand side depended only on (d/dt)²(w-x)? How could you get such an equation?

 

[Astronuc]

What can one say about the center of mass? How does each move with respect to the CM?

Also use \ddot{x} for $$\ddot{x}$$

 

[americanforest]

Are you suggesting I make one equation for both masses instead of two separate equations?

$$x_{cm}=\frac{{m_{1}x_{1}+m_{2}x_{2}}}{{\sum{m}}}$$

$$x_{1}=w, x_{2}=x$$

 

[erogard]

I know this thread is old, but I was wondering if someone could confirm the attempt suggested in the above post.