2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/126526We consider a second-order equation of Duffing type. Bounds for the derivative of the restoring force are given which ensure the existence and uniqueness of a periodic solution. Furthermore, the unique periodic solution is asymptotically stable with sharp rate of exponential decay. In particular, for a restoring term independent of the variable $t$, a necessary and sufficient condition is obtained which guarantees the existence and uniqueness of a periodic solution that is stable.Key words and phrases: Periodic solution, topological degree, stabilityClassical Analysis and ODEs34C25; 34C10text