The stability of a pendulum with two degrees of freedom at the support point is considered. The differential equations for this system are two coupled second order differential equations with a periodic coefficient. The stability of such equations, which describe the motion of a missile on a shock mount, can be studied by the direct method of Liapunov. The basic technique is used to derive the stability criterion coefficients as converging series. The basic technique, however, does not provide a useful solution since too many terms are required for convergence. To avoid this difficulty, it is shown that the series can be summed for the special case considered. The results are therefore derived which can be used with accuracy and for any combination of missile parameters.