  The presence of (approximate) conservation laws can prohibit the fast
relaxation of interacting many-particle quantum systems. We investigate this
physics by studying the center-of-mass oscillations of two species of fermionic
ultracold atoms in a harmonic trap. If their trap frequencies are equal, a
dynamical symmetry (spectrum generating algebra), closely related to Kohn's
theorem, prohibits the relaxation of center-of-mass oscillations. A small
detuning $\delta\omega$ of the trap frequencies for the two species breaks the
dynamical symmetry and ultimately leads to a damping of dipole oscillations
driven by inter-species interactions. Using memory-matrix methods, we calculate
the relaxation as a function of frequency difference, particle number,
temperature, and strength of inter-species interactions. When interactions
dominate, there is almost perfect drag between the two species and the
dynamical symmetry is approximately restored. The drag can either arise from
Hartree potentials or from friction. In the latter case (hydrodynamic limit),
the center-of-mass oscillations decay with a tiny rate, $1/\tau \propto
(\delta\omega)^2/\Gamma$, where $\Gamma$ is a single particle scattering rate.
