Making your animations subtle is very important. This usually means they should be very short, circa 300ms or less. However even a tiny amount of undamped spring means they need more time to feel natural.
Perceived smoothness is a function of distance travelled and the frame rate, so the further the total distance travelled (in any direction, e.g. when bouncing on a spring), the longer the animation must be to appear smooth. Even if it is longer than you would normally like such an animation to be.