  We investigate in details the inertial dynamics of a uniform magnetization in
the ferromagnetic resonance (FMR) context. Analytical predictions and numerical
simulations of the complete equations within the Inertial
Landau-Lifshitz-Gilbert (ILLG) model are presented. In addition to the usual
precession resonance, the inertial model gives a second resonance peak
associated to the nutation dynamics provided that the damping is not too large.
The analytical resolution of the equations of motion yields both the precession
and nutation angular frequencies. They are function of the inertial dynamics
characteristic time $\tau$, the dimensionless damping $\alpha$ and the static
magnetic field $H$. A scaling function with respect to $\alpha\tau\gamma H$ is
found for the nutation angular frequency, also valid for the precession angular
frequency when $\alpha\tau\gamma H\gg 1$. Beyond the direct measurement of the
nutation resonance peak, we show that the inertial dynamics of the
magnetization has measurable effects on both the width and the angular
frequency of the precession resonance peak when varying the applied static
field. These predictions could be used to experimentally identify the inertial
dynamics of the magnetization proposed in the ILLG model.
