digital signal processing problem
Since you have the x/y position for each object it should be fairly straightforward.  Call the position of each $p_1(t)$ through $p_4(t)$.  Subtract the mean from all of them since it sounds like you only care about their movement, not their position.

Once you have done that it should be a fairly simple matter of cross-correlating the position functions.  If the vibration frequencies don't change with time you will only get a strong cross-correlation if the vibration frequencies of the two objects are either the same or quite close to each other.