  We present a model space particle-hole Green's function calculation for the
quadrupole excitations of cold Fermi gas near Feshbach resonance using a simple
model where atoms are confined in a harmonic oscillator potential. Both the
Tamm-Dancoff and random phase approximations are employed. By summing up
exactly the ladder diagrams between a pair of interacting atoms to all orders,
we obtain a renormalized atomic interaction which has well defined and
identical limits as the scattering length tends to $\pm \infty$. The
experimentally observed abrupt rise in the excitation spectrum and its
associated large decay width are satisfactorily reproduced by our calculation.
