  A floating hemisphere under forced harmonic oscillation at very high and very
low frequencies is considered. The problem is reduced to an elliptic one, that
is, the Laplace operator in the exterior domain with standard Dirichlet and
Neumann boundary conditions, so the flow problem is simplified to standard
ones, with well known analytic solutions in some cases. The general procedure
is based in the use of spherical harmonics and its derivation is based on a
physics insight. The results can be used to test the accuracy achieved by
numerical codes as, for example, by finite elements or boundary elements.
