Mass-Spring System and the Pollit-Bizzi Experiment

R. Port, November, 2001

What is a mass-spring system?
A Slinky hanging from your hand is a good example.  It is a simple system of a mass and a spring (and, of course, gravity).  The Slinky will settle at some position, the neural position where gravity acting on the mass balances the spring. The system is controlled by a small number of parameters: the MASS, spring STIFFNESS and DAMPING.  If you shake it, it will oscillate at some frequency, f, determined mostly by the stiffness of the spring. If you start the system by pulling the spring above or below the neutral position, it will oscillate with an amplitude that initially matches the initial deviation.  The farther you pull it up or down when starting it, the
larger the amplitude will be.

If you increase the MASS, it will hang at a lower neutral position and oscillate more slowly (other things being equal). If you increase the STIFFNESS of the spring, it will oscillate faster. Reduce the STIFFNESS and it will slow down.  If you increase the DAMPING, its oscillations will die out more quickly and settle at its neutral position.  If the DAMPING is reduced to zero, it will oscillate forever at frequency f.  The term CRITICAL DAMPING means  sufficient damping to prevent overshoot as the mass approaches the neutral position - that is, it will not oscillate but just asymptotically approach the neutral position.  For controlling damping in the Slinky model, imagine oscillating it under water (which will provide greater damping than using it in air). For even greater damping, imagine using it in a bath of oil or honey.  In honey, Im sure the Slinky would be critically damped: pull it away from its neutral position and it will slowly return to that position without oscillating.

QUESTION:
Now, if the monkey's arm in the Pollit and Bizzi experiment behaves like a mass-spring system with a controllable neutral position,  how does this help us understand how the monkey can move its arm to point the right way without being able to see the arm or get any sensory feedback from it about where it is located and no matter where you artificially place it.