Scalar field cosmologies with a generalized harmonic potential and a matter fluid with a barotropic Equation of State (EoS) with barotropic index $gamma$ for the Locally Rotationally Symmetric (LRS) Bianchi I and flat Friedmann-Lema^itre-Robertson-Wa
lker (FLRW) metrics are investigated. Methods from the theory of averaging of nonlinear dynamical systems are used to prove that time-dependent systems and their corresponding time-averag
