  The concept of periodic boundary conditions (PBCs) is immensely significant
in treating an ideal lattice of infinite extent as a finite lattice. An
explicit usage of PBCs is often found missing in undergraduate texts on
analytical treatment of lattice dynamics. The aim of the present work is to
cover this gap by illustrating the application of Born-von Karman PBCs in
lattice dynamical calculations using a computational approach. The equations of
motion are set up for a linear diatomic lattice with a basis, using the nearest
neighbour approximation. The solution is obtained by implementing fourth order
Runge-Kutta algorithm in python. Fast Fourier Transform (FFT) technique is then
used to obtain the phonon frequency spectrum corresponding to the computed
solutions. Similar computations are extended to obtain the phonon spectrum for
monatomic square and honeycomb lattices under the second nearest neighbour
approximation. The computed results are validated against the analytical ones
in each case. The target group of the present work are the students and
educators at the undergraduate level.
