  We present a study of the spectral properties like the energy spectrum, the
eigenmodes and density of states of a classical finite system of
two-dimensional (2D) charged particles which are confined by a quadratic
potential. Using the method of Newton optimization we obtain the ground state
and the metastable states. For a given configuration the eigenvectors and
eigenfrequencies for the normal modes are obtained using the Householder
diagonalization technique for the dynamical matrix whose elements are the
second derivative of the potential energy. For small clusters the lowest
excitation corresponds to an intershell rotation. The energy barrier for such
rotations is calculated. For large clusters the lowest excitation consists of a
vortex/anti-vortex pair. The Lindeman melting criterion is used to calculate
the order-disorder transition temperature for intershell rotation and
intershell diffusion. The value of the transition temperature at which
intershell rotation becomes possible depends very much on the configuration of
the cluster, i.e. the distribution of the particles between the different
shells. Magic numbers are associated to clusters which are most stable against
intershell rotation. The specific heat of the cluster is also calculated using
