  For a time-dependent $\tau$-periodic harmonic oscillator of two linearly
independent homogeneous solutions of classical equation of motion which are
bounded all over the time (stable), it is shown, there is a representation of
states cyclic up to multiplicative constants under $\tau$-evolution or
$2\tau$-evolution depending on the model. The set of the wave functions is
complete. Berry's phase which could depend on the choice of representation can
be defined under the $\tau$- or $2\tau$-evolution in this representation. If a
homogeneous solution diverges as the time goes to infinity, it is shown that,
Berry's phase can not be defined in any representation considered. Berry's
phase for the driven harmonic oscillator is also considered. For the cases
where Berry's phase can be defined, the phase is given in terms of solutions of
the classical equation of motion.
