A Hanging Rope using Inverse Kinematics

I’ve been studying inverse kinematics (specifically in Making Things Move by Keith Peters) and he covers how to drag and reach using inverse kinematics, I tried extending his reaching example to get a hanging effect by always having the rope/chain reaching for something just beneath it’s grasp. This worked but didn’t look realistic at all.

I was wondering if anyone had any information on the maths behind acheiving this effect properly.