  We present a general discussion of the dipole modes of a heteronuclear
bosonic mixture in a harmonic trap by comparing the prediction of the sum-rule
approach with full Gross-Pitaevskii (GP) calculations. Yet in the range of
interaction in which the mixture is miscible and stable at the mean field
level, $g_{12}^2<g_{11}g_{22}$, we find that there are regimes where the sum
rules displays significant deviations from the GP solution. We provide an
interpretation for this behavior in terms of the Ehrenfest approach, which we
show to be equivalent to the sum-rule approach for dipole excitations.
