  We study the dynamics of a macroscopic object interacting with a dissipative
stochastic environment using an adiabatic perturbation theory. The perturbation
theory reproduces known expressions for the friction coefficient and,
surprisingly, gives an additional negative mass correction. The effect of the
negative mass correction is illustrated by studying a harmonic oscillator
interacting with a dissipative stochastic environment. While it is well known
that the friction coefficient causes a reduction of the oscillation frequency
we show that the negative mass correction can lead to its enhancement. By
studying an exactly solvable model of a magnet coupled to a spin environment
evolving under standard non-conserving dynamics we show that the effect is
present even beyond the validity of the adiabatic perturbation theory.
