  The classical lattice dynamics of honeycomb lattices is studied in the
harmonic approximation. Interactions between nearest neighbors are represented
by springs connecting them. A short and necessary introduction of the lattice
structure is presented. The dynamical matrix of the vibrational modes is then
derived, and its eigenvalue problem is solved analytically. The solution may
provide deeper insight into the nature of the vibrational modes. Numerical
results for the vibrational frequencies are presented. To show that how
effective our method used for the case of honeycomb lattice is, we also apply
it to triangular and square lattice structures. A few suggested problems are
listed in the concluding section.
