how do you create a physics objects that springs back to a default position after being pushed?

picking up and moving around objects with your mouse

Imho, it actually does sounds like a spot on use case scenario for a Physics Constraint angular motor + Physics Handle (that’s what you’re using for holding stuff, right?). Even a simple spring suggested earlier on might do, but you’d use the float variant and only spring on a single axis since the rest is not important.

Perhaps you should spend a bit more time digging into it? And if you ever hit any limitations of the now venerable constraint system (I mean, entire AAA games were made using it…), do look into the experiment plugin. It allows you to set multiple, completely independent control targets and modulate them on the fly. You tell the physics engine where you want to arrive and it will do the rest without you doing the math. Think smart PIDs that you do not need to script yourself.