Unreal Engine's "dynamic mesh" feature let us create a disc and control it's vertices. Using the mouse as input, I loop through points that are a certain radius away from it and apply an offset in the direction it moves. (That offset fades off towards the edges to keep it smooth)
To prevent the mesh from folding over itself, I apply a "mesh smooth" a bunch of times per second. That's what's causing it to "settle back" as you said :D