  We consider a physical system constituted by a finite chain of point masses
consecutively linked by linear springs and dashpots. At one of the end points
acts an external control force aligned with the chain and the system is
observable by the position of the other end point. We show that, whatever is
the number of the point masses, if the sequence of the elastic constants is
proportional to the sequence of the dashpot constants, then the mechanical
system is completely controllable, completely observable, completely reachable
and completely re-construictible, in the sense of control theory.
