  We study evolution of gravitational perturbations of black strings. It is
well known that for all wavenumber less than some threshold value, the black
string is unstable against scalar type of gravitational perturbations, which is
named the Gregory-Laflamme instability. Using numerical methods, we find the
quasinormal modes and time-domain profiles of the black string perturbations in
the stable sector and also show the appearance of the Gregory-Laflamme
instability in the time domain. The dependence of the black string quasinormal
spectrum and late time tails on such parameters as the wave vector and the
number of extra dimensions is discussed. There is a numerical evidence that in
the threshold point of instability the static solution of the wave equation is
dominant. For wavenumbers slightly larger than the threshold value, in the
region of stability, we see tiny oscillations with very small damping rate.
While, for wavenumbers slightly smaller than the threshold value, in the region
of the Gregory-Laflamme instability, we observe tiny oscillations with very
small growth rate. We also find the level crossing of imaginary part of
quasinormal modes between the fundamental mode and the first overtone mode,
which accounts for the peculiar time domain profiles.
