  We have numerically solved the Landau-Lifshitz-Gilbert (LLG) equation in its
standard and inertial forms to study the magnetization switching dynamics in a
$3d$ thin film ferromagnet. The dynamics is triggered by ultrashort magnetic
field pulses of varying width and amplitude in the picosecond and Tesla range.
We have compared the solutions of the two equations in terms of switching
characteristic, speed and energy analysis. Both equations return qualitatively
similar switching dynamics, characterized by regions of slower precessional
behavior and faster ballistic motion. In case of inertial dynamics, ballistic
switching is found in a 25 % wider region in the parameter space given by the
magnetic field amplitude and width. The energy analysis of the dynamics is
qualitatively different for the standard and inertial LLG equations. In the
latter case, an extra energy channel, interpreted as the kinetic energy of the
system, is available. Such extra channel is responsible for a resonant energy
absorption at THz frequencies, consistent with the occurence of spin nutation.
