A mercury drop covered by an aqueous solution which is brought into contact with a metal tip al a fixed potential can be excited to sustained electromechanical oscillations ("beating mercury heart"). The driving force for these pulsations is the electrocapillary effect. We investigated these excitations for the traditional watch glass geometry and for linear and ring-shaped geometries with different lengths and diameters, respectively, varying the potential of the metal tip. We find standing waves in the linear geometry with the number of nodes depending on the potential. In the ring geometry we observe a fast pulsation mode and a slow mode with 2-fold symmetry axis. In addition, we find solitary waves circulating on the ring.