  A satellite galaxy or dark matter subhalo that passes through a stellar disk
may excite coherent oscillations in the disk perpendicular to its plane. We
determine the properties of these modes for various self-gravitating plane
symmetric systems (Spitzer sheets) using the matrix method of Kalnajs. In
particular, we find an infinite series of modes for the case of a barotropic
fluid. In general, for a collisionless system, there is a double series of
modes, which include normal modes and/or Landau-damped oscillations depending
on the phase space distribution function of the stars. Even Landau-damped
oscillations may decay slowly enough to persist for several hundred Myr. We
discuss the implications of these results for the recently discovered vertical
perturbations in the kinematics of solar neighborhood stars and for broader
questions surrounding secular phenomena such as spiral structure in disk
galaxies.
