We studied millimeter-sized aqueous sessile drops in an ambient oil environment in a classical electrowetting configuration with a wire-shaped electrode placed at a variable height above the substrate. Within a certain range of height and above a certain threshold voltage, the drop oscillates periodically between two morphologies where it is either attached to the wire or detached from it. We determine the range of control parameters, wire height, and voltage in which oscillations occur and explain it by a simple capillary model. Furthermore, we analyze the dynamics of the oscillations using high-speed video microscopy and numerical fluid dynamics modeling. We develop a one-dimensional harmonic oscillator model that describes the dependence of the drop oscillations on the relevant intrinsic (surface tension, viscosity, density) and extrinsic (wire height, voltage) parameters.