Page 67 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

Harmonically Excited Vibration Chap. 3
54

At large values of » ! ,( / ) approaches 180°, and the impressed force is
expended almost entirely in overcoming the large inertia force as shown in Fig.
3.1-4(c).
In summary, we can write the differential equation and its complete solution,
including the transient term as
X + 2Coo^x + colx = — sin cot (3.1-10)
n
m
yyj
n
^
sin {cot - (f))
x(t) =
z
( ^ Ÿ
— + u —
L
sin (\/l - -1- (3.1-11)

j
(a) U)/(On « 1 (b) U/UJn = 1 (c) (Jj/u)n » 1
Figure 3.1-4. Vector relationship in foreed vibration.