Ziegler paradox and periodic coefficient differential equations

The Ziegler paradox establishes that: given a stable non-conservative mechanical system with at least two degrees of freedom, if we add a small damping the resulting system may be unstable. In this paper we extend this paradox for systems with one degree of freedom. The result is based on changing periodically the coefficients of the system. Some numerical results are presented for the Mathieu's and Meissner's equations.