  We report on the measurement of the spin-dipole (SD) polarizability and of
the frequency of the SD oscillation of a two-component Bose-Einstein condensate
of sodium atoms occupying the $|3^2S_{1/2}, F=1, m_F=\pm1\rangle$ hyperfine
states. This binary spin-mixture presents the important properties of being, at
the same time, fully miscible and rid of the limit set by buoyancy. It is also
characterized by a huge enhancement of the SD polarizability and by the
consequent softening of the frequency of the SD oscillation, due to the
vicinity to the transition to the immiscible phase. The experimental data are
successfully compared with the predictions of theory.
