The linear normal modes of the atmosphere fall into two categories, the low frequency Rossby waves and the high frequency gravity waves. The elastic pendulum is a simple mechanical system having low frequency and high frequency oscillations. Its motion is governed by four coupled nonlinear ordinary differential equations. We study the dynamics of this system, drawing analogies between its behaviour and that of the atmosphere. The linear normal mode structure of the system is analysed, the procedure of initialization is described and the existence and character of the slow manifold is discussed.