Two masses sliding in a track connected by springs

[akinoshigure]

Two masses m1=100g and m2=200g slide freely in a horizontal frictionless track and are connected by a spring whose force constant is k=.5N/m. FInd the frequency of oscillatory motion for this system.

I don't really know how to go about this problem. I'm assuming that the equation to find the frequency would be
w^2=k/m

I did try making the center of mass, but I wasn't sure if it was even necessary. I ended up with xcom=2/3*d where d is the distance from m1 to m2.

Any help or hints would be great. I just don't feel like banging my head on the desk anymore...

 

[mukundpa]

O.K.
The c.o.m will remain stationary as there is no external force on the system.
Take force constant of that part of the spring only, which is (k d)/(2/3*d) = 3k/2
{?think}
Now with this k find frequency for 100 gm block.

One more way is there. Consider it as two body system and use reduced mass principle.

 

[quasar987]

Start by defining a clever coordinate system and writing the equations of motion. Then you'll have to find a clever way to solve them. hint: Involves a change of variable.

As for "trying to make the center of mass", whatever that means, note that the net force on the system will always be 0, hence the CM will always remain in the same place. This is basically the most important point to realize in defining your clever coordinate system.