The reduction of the oscillations of the magnetosphere to a simple mechanical analogue, which can be analyzed in detail, is accomplished in three stages: (1) The comparison of the wave equations for a dipole field magnetized plasma to those for a rectangular model of the plasmasphere with a unidirectional field -- the important physical characteristics are shown to be independent of the particular geometry chosen; (2) the comparison of the equations in the above hydromagnetic box with those of a mechanical system consisting of a set of oscillators, representing field lines, coupled by a wave propagating medium -- for the symmetric modes with weak ion-cyclotron coupling, the equations for the hydromagnetic and mechanical systems are essentially identical; (3) the simplification of the mechanical system to an elementary wave-oscillator model representing the coupling between resonant poloidal and toroidal modes -- the nature of the motion of this model is independent of the strength of the coupling. In general, the behavior of coupled and uncoupled modes is essentially different. When any coupling is present, steady state solutions, as normally understood, are not possible. (Author).