Page 159 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

146 Systems with Two or More Degrees of Freedom Chap. 5

X

rr)2

Figure 5.5-1.

The system to be solved is shown in Fig. 5.5-1. To avoid confusion with
subscripts, we let the displacements be x and y.
/cj 36 kN/m
/c2 36 kN/m

ATZ j 100 kg
m2 '-=25 kg

/4000N, i > 0
F ■■=
\o, t < 0
Initial conditions:
x = x = y = y = {)
The equations of motion are
100jc - -36,000x + 36,000(y - x)

25y - -36,000(y - x) F F
which can be rearranged to
X = -720x + 360y

y = 1440(x - y) + 160
These equations are to be solved together with the recurrence equations of Sec.
4.7.

't,+ i == X, At^ + 2 x^ - x,_,
y,+ i ==y, + 2y, -y,_,
Calculations for the natural periods of the system reveal that they do not differ