  Three methods to describe collective motion, Random Phase Approximation
(RPA), Wigner Function Moments (WFM) and the Green's Function (GF) method are
compared in detail and their physical content analyzed on an example of a
simple model, the harmonic oscillator with quadrupole--quadrupole residual
interaction. It is shown that they give identical formulae for eigenfrequencies
and transition probabilities of all collective excitations of the model,
including the scissors mode, which is the subject of our special attention. The
exact relation between the RPA and WFM variables and the respective dynamical
equations is established. The transformation of the RPA spectrum into the one
of WFM is explained. The very close connection of the WFM method with the GF
one is demonstrated. The normalization factor of the ``synthetic'' scissors
state and its overlap with physical states are calculated analytically. The
orthogonality of the spurious state to all physical states is proved
rigorously. A differential equation describing the current lines of RPA modes
is established and the current lines of the scissors mode analyzed as a
superposition of rotational and irrotational components.
