Hello

A cable is attached at two (nonemoving)fixpoints. Now the cables midpoint is pulled downward, thereby destroying the catenary curve.

Question: How will the cables center of mass (CM) move: op, down or stay fixed?

My thoughts:

I find it intuituitive that the CM will assume the lowest possible position in the catenary (cosh y) curve, but how can i "proove" this? and is it possible to describe the hight of CM as function of the downward midpoint-displacement?

I also wonder if the catenary curve really is "destroyed" - can one not argue, that catenary curve is just altered to fit the new lowered midpoint?

Thank You