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The concept of ‘effective mass’ is frequently used for the simplification of complex lumped parameter systems (discrete dynamical systems) as well as materials that have complicated microstructural features. From the perspective of wave propagation, it is claimed that for some bodies described as metamaterials, the corresponding ‘effective mass’ can be frequency dependent, negative or it may not even be a scalar quantity. The procedure has even led some authors to suggest that Newton’s second law needs to be modified within the context of classical continuum mechanics. Such absurd physical conclusions are a consequence of appealing to the notion of ‘effective mass’ with a preconception for the constitutive structure of the metamaterial and using a correct mathematical procedure. We show that such unreasonable physical conclusions would not arise if we were to use the appropriate ‘effective constitutive relation’ for the metamaterial, rather than use the concept of ‘effective mass’ with an incorrect predetermined constitutive relation.