Page 80 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

Sec. 3.5 Support Motion 67

Substituting into Eq. (3.5-3), we obtain
mco^Y
Ze~^^ =

k —mar + io)C
and
X = { Z e - ‘^ + Y)e^

k -h io)C
Ye^' (3.5-7)

k —mo)^ + io)C
The steady-state amplitude and phase from this equation are
k^ + (a)c)
(3.5-8)
{k - mo)^) + (coj)
and
mco)
tan ik = (3.5-9)
k {k —mco^) +

which are plotted in Fig. 3.5-2. It should be observed that the amplitude curves for
different damping all have the same value of \X /Y\ =1.0 at the frequency
a)/(o^ = yil.

Figure 3.5-2. Plot of Eqs. (3.5-8) and (3.5-9).