  The longitudinal dipole response of a quantum dot has been calculated in the
far-infrared regime using local spin density functional theory. We have studied
the coupling between the collective spin and density modes as a function of the
magnetic field. We have found that the spin dipole mode and single particle
excitations have a sizeable overlap, and that the magnetoplasmon modes can be
excited by the dipole spin operator if the dot is spin polarized. The frequency
of the dipole spin edge mode presents an oscillation which is clearly filling
factor ($\nu$) related. We have found that the spin dipole mode is especially
soft for even $\nu$ values, becoming unstable for magnetic fields in the region
$1 < \nu \leq 2$. Results for selected number of electrons and confining
potentials are discussed. An analytical model which reproduces the main
features of the microscopic spectra has been developed.
