Vibrational Parameters

You can experimentally determine the two vibrational parameters, natural frequency and damping ratio, from either the free and forced vibrational response of the experimental apparatus.

If you know the model parameters, effective end mass, spring constant, and damping constant, you can estimate these vibrational parameters. Recall that the natural frequency is given by:

(1)     

where:

k is the spring constant and

M is the effective end mass.

Also, the damping ratio is given by:

(2)     

where:

C is the damping constant.

However, without knowing the damping constant, C, explicitly, the damping ratio, cannot be estimated.

Once the natural frequency and damping ratio are determined, you can predict the other important system parameters. The ringing frequency is given by:

(3)     

and the resonant frequency is given by:

(4)     

This section is divided into two areas:

• Free Vibration System Parameters
• Forced Vibration System Parameters