Overdamped
The system returns (exponentially decays) to equilibrium without oscillating.
Critically damped
The system returns to equilibrium as quickly as possible without oscillating.
Underdamped
The system oscillates (at reduced frequency compared to the undamped case) with the amplitude gradually decreasing to zero.
Undamped
The system oscillates at its natural resonant frequency (ωo) without experiencing decay of its amplitude.