Abstract The present study examines the problem of horizontally uniform inertial oscillations in a homogeneous, horizontally unbounded rotating fluid. The analytical solution indicates that these oscillations are damped in time due to viscosity. Numerical calculations using the DuFort-Frankel finite difference scheme indicate that amplifying numerical solutions can exist when high frequency inertial oscillations are present. These positive growth rates are associated with the finite difference second time derivative which is a part of this scheme. The amplifying solutions can be eliminated by using a sufficiently small time step Δt. The existence of such solutions was encountered in a study of three-dimensional Bénard convection in a rotating fluid. The numerical results and primary conclusions of that study are summarized.