All 11 Chapters Covered
SOLUTION MANUAL
,Contents
Preface V
Chapter 2 The Laplace Transform 1
Chapter 3 Mechanical Systems 12
Chapter 4 Transfer-Function Approach to Modeling Dynamic Systems 24
Chapter 5 State-Space Approach to Modeling Dynamic Systems 43
Chapter 6 Electrical Systems and Electromechanical Systems 89
Chapter 7 Fluid Systems and Thermal Systems 111
Chapter 8 Time-Domain Analysis of Dynamic Systems 125
Chapter 9 Frequency-Domain Analysis of Dynamic Systems 152
Chapter 10 Time-Domaim Analysis and Design of Control Systems 176
Chapter 11 Frequency-Domain Analysis and Design of Control Systems 198
iii
,Preface
This Solutions Manual presents solutions to all unsolved B-problems. For some
problems, solutions include more materials than are required in problem statements
to aid the user ofthe book.
The text may be used in a few different ways depending on the course objective
and the time allocated to the course.
Sample course coverages are listed below.
If this book is used as a text for a quarter-length course (with approximately
30 lecture hours and 18 recitation hours), Chapters 1 through 7 may be covered.
Ifthe book is used as a text for a semester-length course (with approximately
40 lecture hours and 26 recitation hours), then the first nine chapters may be
covered or, alternatively, the first seven chapters plus Chapters l 0 and 11 may be
covered.
Ifthe course devotes 50 to 60 hours to lectures, then the entire book may be
covered in a semester.
The instructor will always have an option to omit certain subjects depending on the
course objective.
Katsuhiko Ogata
V
, Solutions to B Problems
CHAPTER 2
. B-2-1. f(t) = 0 t<0
= t e2t t2>0
Note that
tel = ,
s?
Referring to Equation (2-2), we obtain
Fs) = d (Ge))= G tee-?') = 1
(s + 2?
B-2-2.
(a) . t <O
= 3 sin(5t + 45°) t 20
Note that
3 sin (5t + 45°) = 3 sin 5t cos 45" + 3 cos 5t sin 45"
= 2sin 5t + 2 cos 5t
V
So we have
@-4 ,«»-5' /2 s' +5 °
s? +s?
= ____ s+5
2.2+2z5
(b) f,(t) = 0 t<0
= 0.03(1 - cos 2t) t20
F>Gs) = Ir(t)] = 0.03 l- 0.03 s _ 0.12
· s s? +2? s(s? + 4)
1
SOLUTION MANUAL
,Contents
Preface V
Chapter 2 The Laplace Transform 1
Chapter 3 Mechanical Systems 12
Chapter 4 Transfer-Function Approach to Modeling Dynamic Systems 24
Chapter 5 State-Space Approach to Modeling Dynamic Systems 43
Chapter 6 Electrical Systems and Electromechanical Systems 89
Chapter 7 Fluid Systems and Thermal Systems 111
Chapter 8 Time-Domain Analysis of Dynamic Systems 125
Chapter 9 Frequency-Domain Analysis of Dynamic Systems 152
Chapter 10 Time-Domaim Analysis and Design of Control Systems 176
Chapter 11 Frequency-Domain Analysis and Design of Control Systems 198
iii
,Preface
This Solutions Manual presents solutions to all unsolved B-problems. For some
problems, solutions include more materials than are required in problem statements
to aid the user ofthe book.
The text may be used in a few different ways depending on the course objective
and the time allocated to the course.
Sample course coverages are listed below.
If this book is used as a text for a quarter-length course (with approximately
30 lecture hours and 18 recitation hours), Chapters 1 through 7 may be covered.
Ifthe book is used as a text for a semester-length course (with approximately
40 lecture hours and 26 recitation hours), then the first nine chapters may be
covered or, alternatively, the first seven chapters plus Chapters l 0 and 11 may be
covered.
Ifthe course devotes 50 to 60 hours to lectures, then the entire book may be
covered in a semester.
The instructor will always have an option to omit certain subjects depending on the
course objective.
Katsuhiko Ogata
V
, Solutions to B Problems
CHAPTER 2
. B-2-1. f(t) = 0 t<0
= t e2t t2>0
Note that
tel = ,
s?
Referring to Equation (2-2), we obtain
Fs) = d (Ge))= G tee-?') = 1
(s + 2?
B-2-2.
(a) . t <O
= 3 sin(5t + 45°) t 20
Note that
3 sin (5t + 45°) = 3 sin 5t cos 45" + 3 cos 5t sin 45"
= 2sin 5t + 2 cos 5t
V
So we have
@-4 ,«»-5' /2 s' +5 °
s? +s?
= ____ s+5
2.2+2z5
(b) f,(t) = 0 t<0
= 0.03(1 - cos 2t) t20
F>Gs) = Ir(t)] = 0.03 l- 0.03 s _ 0.12
· s s? +2? s(s? + 4)
1
