Homework 5
ME 461 – Summer 10
1. An undamped system is being forced at a frequency that is making the oscillations
very large. The magnification of oscillation is (X*k/f0) = 9.756 (two r values will
cause this, use the larger one). The natural frequency of the system is 100 Hz.
Design a Dynamic Vibration Absorber that will completely eliminate all oscillation in
the primary system with the absorber having a mass less than 1 g. Make sure to state
all defining characteristics of the DVA.
2. Find the natural frequencies and mode shapes for the system below. Explain what the
mode shapes mean physically. Assume the bar has a uniform mass distribution and a
length of 3 meters.
M= 20 kg
K1 = 200 N/m
I = 15 kg*m2
K2 = 300 N/m
3. Determine the M and K matrices for the system modeled below. Show at least the
FBD and EOM for Mass 3.
4. For the M and K matrices below, find the natural frequencies and corresponding mode
shapes. If you use Matlab (I suggest this) print the code you used.
1
0

M  0

0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0 kg

0
4
Useful Matlab commands
eig(A)
0
 4 1  2 0
  1 6  3 0  1


K   2  3 7  2 0  *100 N / m


0  2 8  5
0
 0  1 0  5 11 
gives a vector of eigenvalues from matrix A
[V,D]=eig(A)
gives matrices V and D that give the Eigenvectors and
Eigenvalues of matrix A, respectively
inv(A)
gives the inverse of matrix A
A=[a, b, c; d, e, f; g, h, i]
a
Produces matrix A=  d

 g
b
e
h
c
f 
i 