  We study the static and the dynamic response of coherently coupled two
component Bose-Einstein condensates due to a spin-dipole perturbation. The
static dipole susceptibility is determined and it is shown to be a key quantity
to identify the second order ferromagnetic transition occurring at large
inter-species interaction. The dynamics, which is obtained by quenching the
spin-dipole perturbation, is very much affected by the system being
paramagnetic or ferromagnetic and by the correlation between the motional and
the internal degrees of freedom. In the paramagnetic phase the gas exhibits
well defined out-of-phase dipole oscillations, whose frequency can be related
to the susceptibility of the system using a sum rule approach. In particular in
the interaction SU (2) symmetric case, i.e., all the two-body interactions are
the same, the external dipole oscillation coincides with the internal Rabi
flipping frequency. In the ferromagnetic case, where linear response theory in
not applicable, the system show highly non linear dynamics. In particular we
observe phenomena related to ground state selection: the gas, initially trapped
in a domain wall configuration, reaches a final state corresponding to the
magnetic ground state plus small density ripples. Interestingly the time during
which the gas is unable to escape from its initial configuration is found to be
proportional to the square root of the wall surface tension.
