T1-9 4.0 0.31 3 = 0 0.47 0.63 0.94 1.3 1.6 0.63 0.47 0.31 0 3.0 2.0 1.0 0 0.5 1.0 1.5 2.0 f/fn A F_o/k ( ) ( ) ( ) ( ) k      1 –             +    2 f² ____ f_n² c ___ c_cr f ___ f_n 2 1 –              + 2 F_o __________________________ f² ____ f_n² f ___ f_n 3 ___ 3 2 2 F_o / k ________________________ ( ) f ___ f_n c ___ c_cr 2 ( ) 43²Mf²e ___________________________ k      1 –              +    2 f² ____ f_n² 2 k      1 –             + f² ____ f_n² (        ) 43²Mf²e __________________________ f ___ f_n 3 ___ 3 (        ) 2 2 A =                                                            =                                                                                                                           (6) RESONANCE  — It is seen in Figure 7 that displacement and stress levels tend to build up greatly when the forcing frequency coincides with the natural frequency, the build- up  being  restrained  only  by  damping.  This condition is known as RESONANCE. In  many  cases,  the  forced  vibration  is caused by an unbalanced rotating mass, such as the rotor of an electrical motor. The de- gree of unbalance can be expressed as dis- tance e between the C.G. of the rotor and its axis of rotation. The vertical component of the centrifugal force generated by the unbalanced rotor (mass M) is F_c.f. = M3²e sin 3t =  43²Mf² e sin 23t,  (7) where 3 is angular speed of rotation in rad/ sec  and  f  is  the  number  of  revolutions  per second. In case of vibration excitation by the unbalanced rotor, combining of (6) and (7) re- sults in A =                                        =                                                        =                                                                 ,                        (6a) where m is the total mass of the object. Expression (6a) is plotted in Figure 8 for several values of damping (3). 3.0    Vibration Isolation Although VIBRATION ISOLATION is a very large area of vibration control, there are two most widely used techniques of vibration isolation: –  Reduction of transmission of vibratory or shock forces from the object, in which these forces are generated, to the base; and –  Reduction of transmission of vibratory motions of the base to the work area of vibration-sensitive objects. These techniques are similar, but also quite different. They both deal with TRANSMISSIBILITY or TRANSMISSION RATIO. There are several transmission ratios. Usually these refer to the ratios of the maximum values of the transmitted force or displacement to the maximum values of the applied force or the forced motion. The important direction of transmis- sion is from the object to the base for the force isolation, or from the base to the object for the motion isolation. ( )   ( ) Figure 7    Amplitude-Frequency Characteristics of       Massive Block Motion in Figure 6 f² ____ f_n² f ___ f_n 3 ___ 3 2     1 –              + 2 f² / f_n² __________________________ Me ___ m