On forced capillary-gravity waves in a circular cylinder

Capillary-gravity waves induced by the lateral oscillation of a cylindrical container are considered on Hocking's hypothesis that the surface slope at the contact line is proportional to the vertical velocity. This problem has been considered by Shen, Sun and Hsieh on Evans's hypothesis that the surface slope at the contact line is prescribed and proportional to the excitation. The latter condition, in contrast to that of Hocking, leaves the normal modes and resonant frequencies unchanged from those of the classical problem (for which the surface slope vanishes at the contact line), and is conservative (whereas Hocking's condition implies dissipation).