The exact equations of motion of a pneumatic spring are derived. Both single sided and double sided springs are considered. The enclosing walls are assumed to be perfectly rigid. It is shown that the single sided spring exhibits marked asymmetric response when set into motion by a non-zero initial displacement. The peaks are sharp and the troughs are flattened. The amplitude of motion is different in positive and negative directions. The two sided spring gives a symmetric response but the peaks and troughs show sharp corners indicating non-linear response. It is shown that the mounted frequency depends upon only two system parameters, namely, the initial volume and the spring area in contrast to the existing linear theory in which it depends upon two additional parameters, namely, the initial pressure and the mounted mass. The dependance of period of oscillation on the amplitude of initial displacement is demonstrated.

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