Existence of periodic solutions of a generalized friction oscillator

We study the differential equation x″+g(x′)+μ(x)sgnx′+f(x)=φ(t) with TT-periodic right-hand side, which models for example a mechanical system with one degree of freedom subjected to dry friction and periodic external force. If, in particular, the damping term gg is present and acts, up to a unbounded difference, we get the existence of a TT-periodic solution.