Transient nonlinear localization in a system of two rods coupled with a nonlinear backlash spring is studied in this work. The method of Karhunen-Loeve (K-L) decomposition is then used to reduce the order of the dynamics, and to study nonlinear effects by considering energy transfers between leading K-L modes. In addition, the computed K-L modes are used to discretize the governing partial differential equations, thus creating accurate and computationally efficient low-dimensional nonlinear models of the system. Reconstructions of transient nonlinear responses using these low dimensional models reveals the accuracy of the order reduction.