Page 163 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

150 Systems with Two or More Degrees of Freedom Chap. 5
FORTRAN PROGRAM

J TIME DISPL. X, cm DISPL. Y, cm
27 0.2600 16.813269 26.109001
28 0.2700 15.439338 21.370152
29 0.2800 13.723100 17.377266
30 0.2900 11.644379 14.458179
31 0.3000 9.247756 12.733907
32 0.3100 6.643715 12.107629
33 0.3200 3.997202 12.294546
34 0.3300 1.505494 12.886645
35 0.3400 -0.630690 13.439858
36 0.3500 -2.237630 13.566913
37 0.3600 -3.195051 13.018113
38 0.3700 -3.453777 11.734618
39 0.3800 -3.041385 9.863994
40 0.3900 -2.054909 7.734994
41 0.4000 -0.642020 5.796249
42 0.4100 1.025759 4.530393
43 0.4200 2.782778 4.359870
44 0.4300 4.496392 5.562246
45 0.4400 6.086507 8.211138
46 0.4500 7.533995 12.154083
47 0.4600 8.876582 17.031736
48 0.4700 10.193198 22.335049
49 0.4800 11.579966 27.489933
50 0.4900 13.122614 31.953781
51 0.5000 14.870770 35.305943

5.6 VIBRATION ABSORBER
As a practical application of the 2-DOF system, we can consider here the
spring-mass system of Fig. 5.6-1. By tuning the system to the frequency of the
exciting force such that = k 2/ m 2, the system acts as a vibration absorber and
reduces the motion of the main mass to zero. Making the substitution
T /c 1 2 ^2
(0 11
ni2
and assuming the motion to be harmonic, the equation for the amplitude can
be shown to be equal to

^1^1 I ^22.
(5.6-1)
0 k-,
1 + — 1 - ( - ) 1
1^11 / [(Oil I
Figure 5.6-2 shows a plot of this equation with ¡jl = m 2/m , as a parameter. Note