Results are presented of particle simulations of the time‐dependent behavior of the plasma sheath surrounding an electrode whose potential is abruptly changed from 0 to some negative value. The surrounding plasma is assumed isotropic and collisionless, and the electrode is a sphere or infinite cylinder. Potential steps up to −1000kTe/eare considered. The time histories and frequency spectra of sheath and plasma oscillations initiated by the potential step are studied. The energy in sheath oscillations (frequency <&ohgr;p) escapes by nonlinear coupling to plasma oscillations (frequency &ohgr;p). The time scale for sheath–plasma coupling depends strongly on the ion‐to‐electron mass ratio. Both linear and nonlinear ion acoustic waves are excited by the response to the potential step. Near a small (radius 1&lgr;D) cylindrical electrode, trapped ions are shown to make an important contribution to the sheath ion density. The height of the transient peak in collected current for a cylindrical electrode displays strong dependence on the ion‐to‐electron temperature ratio, for sufficiently large potential steps.