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

Dipole modes of a trapped bosonic mixture: Fate of the sum-rule approach