  This article concerns the stability of a model for mass-spring systems with
positive damping and negative stiness. It is well known that when the
coefficients are frozen in time the system is unstable. Here we find conditions
on the variable cofficients to prove stability. In particular, we disprove the
believe that if the eigenvalues of the system change slowly in time the system
remains unstable. We extend some of our results for nonlinear systems.
