This paper describes a preliminary investigation into the use of normal form theory for modelling large non-linear dynamical systems. Limit cycle oscillations are determined for simple two-degree-of-freedom double pendulum systems. The double pendulum system is reduced into its centre manifold before computing normal forms. Normal forms are obtained using a period averaging method which is applicable to non-autonomous systems, more advantageous than the classical methods. Good agreement is observed between the predicted results from the normal form theory and numerical simulations of the original system.