  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.
