Stability of Solutions to Damped Equations with Negative Stiffness

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.