  The numerous phenomenological equations used in the study of the behaviour of
single-domain magnetic nanoparticles are described and some issues clarified by
means of qualitative comparison. To enable a quantitative \textit{application}
of the model based on the Debye (exponential) relaxation and the torque driving
the Larmor precession, we present analytical solutions for the steady states in
presence of circularly and linearly polarized AC magnetic fields. Using the
exact analytical solutions, we can confirm the insight that underlies
Rosensweig's introduction of the "chord" susceptibility for an approximate
calculation of the losses. As an important consequence, it can also explain
experiments, where power dissipation for both fields were found to be identical
in "root mean square" sense. We also find that this approximation provides
satisfactory numerical accuracy only up to magnetic fields for which the
argument of the Langevin function reaches the value 2.8.
