  The resonant and non-resonant effects of core plasma on the excitation of low
frequency modes with $\omega < \omega_{BAE}$, such as Beta-induced Alfv\'en
Acoustic Eigenmodes (BAAEs) and Kinetic Ballooning Modes (KBMs) are examined in
the framework of the generalized fishbone-like dispersion relation. The
formalism of the fishbone-like equation contains all the necessary ingredients
to describe the features of these low frequency fluctuations, and explain
experimental findings. Core plasma properties (diamagnetic frequency and
precession resonance with trapped ions) strongly affect the excitation of the
modes, and in the case of BAAEs more effectively than the energetic particles.
The diamagnetic frequency of the core plasma also contributes to the coupling
of the BAAEs with the KBMs, thus affecting the excitation and polarization of
both modes. Energetic particles can still provide a non-resonant drive to some
of the low frequency modes.
