  We derive expressions for the dynamical matrix of a crystalline solid with
total potential energy described by an embedded-atom-method (EAM) potential. We
make no assumptions regarding the number of atoms per unit cell. These
equations can be used for calculating both bulk phonon modes as well the modes
of a slab of material, which is useful for the study of surface phonons. We
further discuss simplifications that occur in cubic lattices with one atom per
unit cell. The relationship of Born-von-K\'arm\'an (BvK) force constants -
which are readily extracted from experimental vibrational dispersion curves -
to the EAM potential energy is discussed. In particular, we derive equations
for BvK force constants for bcc and fcc lattices in terms of the functions that
define an EAM model. The EAM - BvK relationship is useful for assessing the
suitability of a particular EAM potential for describing vibrational spectra,
which we illustrate using vibrational data from the bcc metals K and Fe and the
fcc metal Au.
