  The response of spin-2 small condensates to an external magnetic field $B$ is
studied. The parameters of the interaction are considered as variable. The
emphasis is placed on clarifying the modes of excitation caused by the
quadratic Zeeman term. The theoretical method used is beyond the mean field
theory. A set of eigenstates with the $U(5)\supset SO(5)\supset SO(3)$ symmetry
is introduced to facilitate the analysis. To obtain a quantitative evaluation
on the response, the fidelity susceptibility and the $B$ -dependent average
populations of spin-components have been calculated. Mostly the particle number
N=30 is assumed. The effect with a larger or smaller $N$ is also considered. It
was found that the sensitivity of the response depends strongly both on the
interaction and on the inherent symmetry.
