This thesis describes the analytical study of a structural system under the combined action of noncirculatory or circulatory loading and oscillating base motion. The model is a double inverted pendulum composed of two rigid weightless bars of equal length with two concentrated masses at the ends of each bar, on an oscillating base. Noncirculatory or circulatory loading is applied at the free end. At the hinges restoring moments are produced by spring and damping forces. Damping coefficients are taken as positive, and gravitational effects are considered. The stability of the system under the combined action of the noncirculatory or circulatory loading and the parametric excitation can be investigated by Hsu's method. This method is applied to solve the coupled Mathieu equations by the given system and determine the unstable resonance, a nonlinear analysis is used to find the steady state response. / Thesis / Master of Engineering (MEngr)