Not sure how helpful this is but it shows how to drive the kinematics of
a 'Follower' null with a spring constraint acting on its ICE Kinematics.
It requires a simulated tree. I don't think there's any way of producing
the same effect without simulation. With only a modeling stack you only
have access to the current frame's data. To use just press play and drag
the 'Master' null around. You can play with damping, mass and stiffness.
There's also an example of a projectile simulation (using the standard
particle system and Simulate Particles) compared with a Null which has
it's kinematics driven by a hand-built 'simulate' compound using a basic
Euler integration technique (the same one, I think, they use in the
built-in compound). All the concepts are directly transferable e.g. in
this example both systems use the built in Gravity force and it works in
the same way.
Scene (2013 SP1) here:
https://dl.dropboxusercontent.com/u/69741069/jj_spring_null_euler.rar
Julian