Adjustable Z Length of a Simple Catenary System

Does anyone know how I can vary the z axis on this catenary system so that the heights are adjustable parametrically?  Do I need to introduce an attractor? For example, if I wanted them to follow the shape of a "s" curve and vary the lengths in the z axis based on that "s" shape, how would I go about doing that?  I am new at this and am missing the most basic component that makes this object parametric in the z axis. Please see attached image.  Any input would be great!