The coupled equations of motion describing electrostatic plasma oscillations
are derived using a collective coordinate approach. The
boundary between the physical and nonphysical regions of phase space
is discussed. The two mode case is studied in detail for both small
and large initial disturbances. For small initial disturbances the
motion was found to be periodic. For large initial disturbances, non-periodic
growing solutions were found that approached one of two
asymptotic limits. For these solutions, the variables became infinitely
large in a finite time.