  A mechanical system consisting of water covered by brash ice and a body
freely floating near equilibrium is considered. The water occupies a half-space
into which an infinitely long surface-piercing cylinder is immersed, thus
allowing us to study two-dimensional modes of the coupled motion which is
assumed to be of small amplitude. The corresponding linear setting for
time-harmonic oscillations reduces to a spectral problem whose parameter is the
frequency. A constant that characterises the brash ice divides the set of
frequencies into two subsets and the results obtained for each of these subsets
are essentially different.
  For frequencies belonging to a finite interval adjacent to zero, the total
energy of motion is finite and the equipartition of energy holds for the whole
system. For every frequency from this interval, a family of motionless bodies
trapping waves is constructed by virtue of the semi-inverse procedure. For
sufficiently large frequencies outside of this interval, all solutions of
finite energy are trivial.
