The relaxation of a rigid particle suspended in a one-dimensional oscillating flow is calculated according to different drag models and the results are compared. Conditions are derived under which relaxation can be neglected or drag models can be substituted by simpler ones. This investigation is conducted analytically and graphically via the plane defined by the Reynolds number and amplitude parameter. This work matches various, mostly analytic drag models together to consider simple particle relaxation with a few, broad range input parameters and cover large parts of the plane spanned by Reynolds number and amplitude parameter.