Partial List of Errata
(Updated March 17, 2009)
Theory of Vibration with Applications, Thomson, W. T.,
and Dahleh, M. D., 5th. Ed., Prentice-Hall, 1998.
(First printing)
p. xii Third para., line 6
“Polinomial” should read “Polynomial”.
p. xii Third para., line 7
“Diogonalization” should read “Diagonalization”.
p. 9
First para., line 6
“Fig. 1.2.1.” should read “Fig. 1.2.1 if the ratios of the
natural frequencies are rational numbers.
p. 9
Equation (1.2.1)
The notation used in this equation is unconventional.
Replace the equation with:
x t  
a0
 a1 cos  t  a 2 cos 2 t  
2
 b1 sin  t  b2 sin 2 t  
where

2

.
p. 9
Two lines immediately
following above Eq. (1.2.1)
Replace “ n ” with “ n ”, and “  m ” with “ m ”.
p. 9
Equation (1.2.2) to
Equation (1.2.8)
Replace in all cited equations “ n ” with “ n ”, and
“  m ” with “ m ”.
p. 11
First para., line 1
Replace “ n ” with “ n ”.
p. 18
Example 2.2.1
“f” should read “ f n ”.
p. 19
Example 2.2.3, line 3
“polar” should read “mass”.
p. 20
Line 1
“polar” should read “mass”.
p. 20
Example 2.2.4, line 2
“spring forces” should read “initial compressive spring
forces”.
1
p. 20
Example 2.2.4, line 3 of Solution
A clockwise arrow with a + sign should
precede the summation sign.
p. 22
Example 2.3.2, line 3
r  R should read r  R .
p. 22
Example 2.3.2, line 3 of Solution
“rotational” should read “absolute rotational”.
p. 23
Example 2.4.1, line 1
“mass of the spring” should read “uniformly distributed total
mass of the spring, ms ,”.
p. 24
Example 2.4.2, line 1
“beam of total” should read “beam of uniformly distributed
total”.
p. 24
Example 2.4.2, Figure 2.4.2
Add a vertical downward arrow to the left of M,
starting from the horizontal line and ending at the beam, and
label it y.
Add a vertical downward arrow to the right of the beam,
starting from the horizontal line and ending at the same
level as the bottom of M, and label it y M . Change y max in
the equations to y M .
p. 24
Example 2.3.2, line 4 of Solution
Remove the word “maximum”.
p. 24
Example 2.3.2, line 5 of Solution
Tmax should read Tadd .
p. 29
Mid-page para., line 1
“along the horizontal axis” should read “as a parameter”.
p. 31
Sect. 2.7, line 1
“in a” should read “in an underdamped”.
p. 33
Example 2.7.2, line 2 of Solution
x n 1 
x
e should read n 1  e  .
xn
xn
p. 36
Item 11, figure
y should label a downward arrow from horizontal line to
beam.
p. 36
Item 11, right column
yx 
Pbx 2

l  x 2  b 2  should read
6 EIl
y x  
Pbx 2
l  x 2  b 2  for 0  x  a .
6 EIl
2
p. 41
Fig. P2.22
k2 should read k .
p. 44
Prob. 2.38, line 3
Prob. 2.40, line 2
Prob. 2.41, line 2
Prob. 2.42, line 2
Remove the word “natural”.
Remove the word “natural”.
Remove the word “natural”.
Remove the word “natural”.
p. 49
First para., line 1
“is forced” should read “tends”.
p. 50
Figure 3.1.2.
The horizontal “Reference” line is missing.
The arrow for  should be directed from vector F0 to vector
X.
p. 53
Middle of page
After “ H   depends only on”, insert “the stiffness k, ”.
p. 53
Eq. (3.1.17)
“ H   ” should read “ kH   ”.
p. 64
Eq. (3.5.8)
This equation should read:
p. 64
Next to last line
Drop the absolute value sign for X Y .
p. 65
Figure 3.5.2
Drop the absolute value sign for X Y .
p.65
Second para., line 1
Drop the absolute value sign for X Y .
p. 66
Figure 3.6.1
Arrow for  should be directed clockwise.
p. 66
First line
“transmitted” should read “amplitudes of the transmitted”.
p. 66
First two equations
Remove absolute value signs.
p. 66
Last two equations
Enclose expressions within absolute value signs.
p. 71
Example 3.8.1
Limits of first integral should be –X and X.
p. 72
In Solution
Fourth equation should read:
3
X

Y
k 2  c 
2
k  m   c 
2 2
2
2
X 
 4F 
F  d 
    F0
k  m 2 2 k
2
0
2
 4F 
1   d 
 F0 
2
   2 
1    
   n  
p. 74
Sect. 3.10, title
“OR” should read “OF”.
p. 74
Second para., line 1
“ xres ” should read “ X res ”.
p. 74
Second para., line 3
“referred to” should read “referred to, when   1 ,”.
p. 75
Figure 3.10.1
“
p. 75
Figure 3.10.1
Horizontal dimension “ 2 ” should read “2 n ”.
p. 75
Line before Eq. (3.10.4)
“Q” should read “Q, known as quality factor,”
p. 75
Line after Eq. (3.10.4)
Insert before “Here …” the following: “It can be shown,
from examining power dissipation, that Eq. (3.10.4) is valid
for all values of  ."
p. 75
Space below Eq. (3.10.5)
Section “3.11 RESPONSE TO PERIODIC FORCES” from
the 1981, 2nd Ed., belongs here! Why this section was
removed after the 2nd Edition is incomprehensible,
especially since all editions treat Fourier series in Chapter 1.
The corrections listed above for pages 9 and 11 apply to this
section as well, i.e., replace “  1 ” with “  ”, and “ n ” with
“ n ”.
p. 77
Figure 3.11.2
Drop the absolute value sign for Z Y .
p. 81
Example 3.11
Add to problem statement: “Assume  n  0.2 .”
p. 89
First para., line 3
Add after the word “produced” the following: “when
damping is present.”
X
X
” should read “
”.
X0
F0 k
Change “Such” to “such” and add before it the following:
“For an undamped system,”
p. 95
First line below Eq. (4.3.1a)
Replace “forced vibration” with “forced vibration, which is
known as the zero-state response,”
4
p. 95
Second line below Eq. (4.3.1a)
Replace “initial conditions” with “initial conditions, which is
known as the zero-input response.”
p. 95
Eqs. (4.3.1c) and (4.3.1d)
Replace “z(s)” with “Z(s)”.
p. 96
Line below x(t ) equation
“  2 ” should read “ n2 ”.
p. 98
Line below Eq. (4.4.4)
1
1

” t   .” should read “ t   , if t1  .”
2
2
2
p. 99
Line below Eq. (4.4.10)
“with” should read “with an identical term added but with”.
p. 99
Eq. (4.4.11)
Replace “ t ” in the sine and cosine terms with “ t  ”.
p. 103 Line above Eq. (4.5.4)
“Eq. (4.4.6)” should read “Eq. (4.4.10)”.
p. 104 Line below Fig. 4.5.6
“Eq. (4.4.6)” should read “Eq. (4.4.12)”.
p. 119 Figure P4.12
Bottom formula should have a minus sign in front it.
p. 128 3rd & 5th lines from bottom
Remove “(x)” from the “  ’s”.
p. 133 Figure 5.2.1
“ 2 ” should read “ 2 b ”.
p. 144 Middle of page
“two natural frequencies exist” should read “two natural
frequencies 1 and 2 exist.
p. 145 Figure 5.6.3
Title should read “Natural frequencies 1 (lower branch) and
2 (upper branch) vs.   m2 m1 .”
p. 156 Figure P5.29
Add “t” to “ sin t ”.
p. 178 Orthonormal modes
The nomenclature used here by the author is unconventional.
When a natural mode or mode shape is normalized, it gets
the name “normal mode.” This is true whether the mode is
normalized by setting one element of the eigenvector equal
to unity, or by adjusting the elements of the eigenvector so
that the “generalized mass” equals unity. Normal modes are
always orthogonal for distinct eigenvalues, and they can be
orthogonalized for repeated eigenvalues. Therefore, the term
“ortho” before “normal” is really unnecessary.
p. 180 Example 6.7.1
The matrix equation for P T MP has a scalar multiplier m
missing from the mass matrix, and in the result that follows.
5
1
~
The matrix equation for P has a scalar multiplier
m
missing from both matrices.
p. 181 Top of page
The matrix equation for PT KP has a scalar multiplier
k
m
missing from the triple matrix product, and the result.
p. 182 Example 6.8.2
The matrix equations for M 1 and M 2 have a scalar
multiplier m missing from the mass matrix, and in the results
that follow.
1
~
The matrix equation for P has a scalar multiplier
m
missing.
p. 184 Entire page
The definition of x here is confusing. The symbol x is used
in two different ways. One definition of x is as a position
coordinate measured upward along the building starting from
the base. In this case xi identifies the location of the ith
floor. Another way xi is used here is to define the transverse
displacement of the ith floor. It would have been better if the
author had used ui for this latter purpose.
In keeping with the notation on p. 179, Eq. (6.7.1), the vector
in Fig. 6.10.1 containing the list of x’s should have a
superscript (1) instead of a subscript 1.
p. 185 5th line
“(p(x)f(t)” should read “p(x)f(t)”.
p. 185 Equation (6.10.6)
“P” should read “p”.
p. 187 Top of page
Add “  12 q1 ” to the expression on the left-hand side.
p. 467 Eq. (B.14)
“ C1 ” should read “ C12 ”.
p. 468 Item (18)
Add “   1 ” to the right of inverse function.
p. 507 2.56
“2/3” should read “4/9”.
6