We have recently shown that the low-temperature velocity power spectrum of an anharmonic oscillator (AHO) in a canonical ensemble is recovered when one considers the AHO as coupled via harmonic springs to a system of noninteracting harmonic oscillators (HO’s), each with the same characteristic frequency as that of the AHO [D.P. Visco, Jr. and S. Sen, Phys. Rev. E 57, 224 (1998)]. In the present work, we generalize our earlier study by establishing the following points. (i) We show that when the AHO is coupled via anharmonic springs to a system of noninteracting HO’s, each with characteristic frequency as that of the AHO, the dynamics of the AHO is strongly affected by the altered coupling and hence we contend that the bath particles must be connected via harmonic springs to preserve the dynamics of the AHO. (ii) We consider an AHO with a characteristic frequency that differs from that of the bath particles and show that the correct dynamics of the new AHO is recovered when (a) the harmonic oscillators that make up the bath particles have constrained movement and (b) the bath particles are harmonically coupled at significantly weakened strength compared to the study in case (i) above. © 1998 The American Physical Society.