Physics education research, electronic materials, and the musings of Christopher Moore, Ph.D.

Suppose you have two objects attached to a string.  For simplicity's sake, suppose the string does not stretch and retains a constant length of L.  Now suppose a force acts on one of the objects so that in the next time interval, so to speak, it moves from point (a, b) to (a`, b`).  The other object starts at (x, y) and ends at (x`, y`).  Now my question is where does the other object go in that interval of time in terms of L, a, b, a`, b`, x, and y?

I'm pretty sure it takes some calculus to do, but that aside, I drew a circle around (c, d) with the radius being the string's length.  Then I attempt to find the point at which the distance from (x, y) to (x`, y`), the latter being on the circle, is a minimum.  But I'm not quite sure if that is correct, and even then, how would I get what (x`, y`) is?

This is probably both a math/physics question, but I need to know the physics before doing the math.

Thank you!