The transverse dynamics of a 28.5-GeV electron beam propagating in a 1.4 m long, (0-2)x10(14) cm(-3) plasma are studied experimentally in the underdense or blowout regime. The transverse component of the wake field excited by the short electron bunch focuses the bunch, which experiences multiple betatron oscillations as the plasma density is increased. The spot-size variations are observed using optical transition radiation and Cherenkov radiation. In this regime, the behavior of the spot size as a function of the plasma density is well described by a simple beam-envelope model. Dynamic changes of the beam envelope are observed by time resolving the Cherenkov light.