  We discuss the appearance of oscillatory and standing wave states in
second-order oscillator networks showing that it is a special case of a more
general mechanism involving secondary synchronized clusters induced by inertia.
Using a time-periodic mean-field ansatz, we find a bistable mechanism involving
a stable fixed point and an invariant curve of an appropriate Poincar\'e map.
The bistability and the devil's staircase associated to the rotation number on
the invariant curve provide an explanation for the appearance of the secondary
synchronized clusters. The effect of inertias in the self-organization process
is analyzed through a simplified model. This shows that the effect of giant
synchronized clusters on the other oscillators is weakened by inertias, thus
leading to secondary synchronized clusters during the transition process to
synchronization.
