We consider the effects of bath size on the nature of the dynamics and tran
sport properties for two simple models in which the bath is composed of a c
ollinear chain of harmonic oscillators. The first model consists of an untw
isted rotating chain (elastic rotor) for which we obtain a non-Markovian eq
uation analogous to the generalized Langevin equation for the rotational de
grees of freedom. We demonstrate that the corresponding memory function osc
illates with a frequency close to that of the lowest mode of the chain. The
second model considered consists of a tagged oscillator in a finite harmon
ic chain. For this model, we find an additional harmonic force in the gener
alized Langevin equation for the terminal atom that does not appear in the
equation of motion for the semi-infinite chain. It is demonstrated that the
force constant for the additional harmonic force scales as 1/N, where N is
the number of oscillators in the chain. Using an exact representation for
the velocity correlation function, the transport properties of the model ar
e discussed.