  The solution of the Feinberg-Horodecki (FH) equation for a time-dependent
mass (TDM) harmonic oscillator quantum system is studied. A certain interaction
is applied to a mass to provide a particular spectrum of stationary energies.
The related spectrum of the harmonic oscillator potential acting on the TDM
oscillators is found. We apply the time version of the asymptotic iteration
method (AIM) to calculate analytical expressions of the TDM stationary state
energies and their wave functions. It is shown that the obtained solutions
reduce to those of simple harmonic oscillator as the time-dependent of the mass
reduces to
