Undamped Free Response

Free vibration occurs because there is an initial disturbance to the system. The initial disturbance is referred to as an initial condition, which can be either a displacement of the mass, an initial velocity of the mass, or both. Frequency of the system is determined by the mass and spring constant of the system, initial conditions do not affect the vibration frequency of an undamped system, therefore it is called the natural frequency. Vibration amplitude and the phase angle are also determined by initial conditions. Theoretically, an undamped free vibration system will vibrate forever once it is started.

DANIEL J. INMAN, Engineering Vibration, Prentice Hall, Englewood Cliffs, New Jersey,1994