If m1 and m2 are on a bar, Can the forces heir forces be computed, give a third mass m3 acting gravitationally?

Question

The simple problem of 2 masses m1 and m2, joined by a bar (constant distance between them), and a third body (outside the bar) m3.

O(m1)
\
\ O(m3)
O(m2)

All masses and positions are known.

From the system center of mass: [Xcm,Ycm] = [x1m1+x2m2+x3m3, y1m1+y2m2+y3m3]/(m1+m2+m3), How can I write: d^2(r2)/dt^2 [The acceleration (or force) over m2], in cartesian [X,Y] coordinates ?

I know the bar will "feel" m3, generating a force over its center of mass; but I don't how to keep going to get d^2(r2)/dt^2.