  The fact that the ground-state first-order density matrix for Bosons in a
parabolic potential with interparticle harmonic interactions is known in exact
form is here exploited to study collective excitations in the weak-coupling
regime. Oscillations about the ground-state density are treated analytically by
a linearized equation of motion which includes a kinetic energy contribution.
We show that the dipole mode has the frequency of the bare trap, in accord with
the Kohn theorem, and derive explicit expressions for the frequencies of the
higher-multipole modes in terms of a frequency renormalized by the
interactions.
