Harmonic noise (also called quasimonochromatic noise) is used as an ex
ternal stochastic source term in a non-Markovian oscillatory system wi
th memory-damping. The stationary second moments are obtained by using
the adjoint Fokker-Planck operator method. If the internal noise is h
armonic then the occurrence of two maxima in the mean energy of the dr
iven system seems to be obvious and depends on the seclected relations
of the frequencies of the three oscillators. The effects of the frequ
ency-dependent strength of the external harmonic noise on the resultin
g energy and some generic cases like the interactions between internal
harmonic noise and external white noise or exponentially correlated n
oise have been investigated.