This research focuses on scalar field cosmologies with a generalized harmonic potential. Our attention is centred on the anisotropic LRS Bianchi I and III metrics, Bianchi V metrics, and their isotropic limits. We provide a comprehensive overview of the first two metrics classes and offer new findings for Bianchi V metrics. We show that the Hubble parameter is a time-dependent perturbation parameter that controls the magnitude of the error between full-system and time-averaged solutions as it decreases, such that those complete and time-averaged systems have the same asymptotic behaviour. Therefore, oscillations entering the system can be controlled and smoothed out, which simplifies the problem at hand.