Destabilization via active stiffness

In a recent paper leit one of the authors noted, without presenting aproof, that appropriate variation of the stiffness coefficient in amass-spring-damper system leads to increase of the system energy during acycle of the motion. Some have expressed doubt concerning the validity ofthis claim which implies that a damped simple oscillator can be destabilizedby varying the spring constant. It is the purpose of this note to present aproof