How to graph the displacement of an atom? (formula below)

u(jl,t)=Σ U(j,k,v)exp(i[k*r(jl)-⍵(k,v)t])

the displacement of the jth atom in the lth unit cell.

Sum of all wave vectors, k, and over all branches in the dispersion diagram, v. U(j,k,v) is amplitude vector that tells how atom j moves under the influence of the wave(k,v). r(jl) is the equilibrium position of the atom (jl) or origin of the unit cell (l).

i is complex number. ⍵ is natural frequency, so ⍵(k,v) is natural frequency of the wave (k,v) t is time

Additional explanation: (pg 85, equation 6.18) https://books.google.com/books?id=jpe2aYwF3v0C&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false

http://fropho.sourceforge.net/doc/node84.html