Underdamped response with  where the excitation frequency is twice the natural frequency. Transient effects die out almost immediately after which the system vibrates at a steady-state.

An underdamped system with very low damping (), where the system is excited at its natural frequency.

An undamped system is excited at its natural frequency, which results in resonance.

Underdamped response with  where the excitation frequency is ten times lower than the natural frequency.

Underdamped response with , where the excitation frequency is twice the natural frequency. Some transient behaviour is observed before the system reaches a steady-state.

An undamped system excited very close to its natural frequency, which exhibits beating behaviour.

An undamped forced response with two distinct frequencies of vibration - one which corresponds to the excitation frequency, and the other which corresponds to the natural frequency of the system. 

Underdamped response of a system with , where the system is excited at the natural frequency.