  We consider a forced oscillation and passage through resonance for an
infinite-length system, having time-varying parameters and possessing a single
trapped mode. The system is a string, lying on the Winkler foundation and
equipped with a discrete linear mass-spring oscillator of time-varying
stiffness. We obtain the principal term of the asymptotic expansion for the
resonant solution describing the motion of the inclusion (i.e., the mass-spring
oscillator). The obtained result was verified by independent numerical
calculations based on solution of the corresponding partial differential
equation by means of the method of finite differences. The comparison
demonstrates a good agreement in a neighbourhood of the instant of resonance.
