HW for Multi-DOF System
!!Please submit it on Oct.19
1.The 1/4 vehicle model is shown in Fig.1 for the following
parameters: Mb=317.5kg,Mw=45.4kg, kt=192000N/m, ks=22000N/m，
C＝1520Ns/m. Derive the equation of motion and find the natural
frequencies.
Fig.1
2. The coupled pendulums shown in Fig.2 have the same
parameters. When the left pendulum is disturbed by giving it an
initial angle  0 , determine the free vibration response of the system.
(15 points)
a
L
k
m
Fig.2
c
m
3. Determine the natural frequencies and normal modes of the
torsional system shown in Fig. 3 for kt2=2kt1 and J2 = 2J1. (10 points)
Fig.3
4. please apply the software MATLAB to find the natural
frequencies and natural modes of the 1/4 vehicle model in Fig.1
and the half-car model in Fig.4.
a=1.25m;b=1.51m;
mb=690kg; jb=1222 kgm2;
mwf=40.5 Kg;
ksf=17000 N/m; ksr=20000 N/m;
Fig.4
mwr=45.4 Kg;
ktf =192000 N/m;
ktr =ktf;