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 of the 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.
                If the 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 10 and 11 may be
             covered.
                If the 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
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                                                     v
               Solutions to 8 Problems
                                   CHAPTER 2
 B-2-1.                             f(t) = 0                         t   <. 0
                                            =    t ·e-2t             t   >o
 Note that
                                       oG (t)         = __l
                                                         s2
 Referring to Equation (2-2), we obtain
                          F(s) = � [f(t)] =                 rl     [t e-2tJ = _l__
                                                                              (s + 2)2
--------------------------------· -----------------------------·
B-2-2.
(a)                                                                              t    <O
                                             =   3 sin ( St + 45 c)              t   zO
Note that
                 3 sin ( St + 45 °)         = 3 sin St cos 45 ° + 3                   cos St sin 45    e
                                            = 2- sin St + _L cos                      St
                                              J2           J2
So we have
                  .
                      Fl (s)   =   l [fl(t)]         =   _3_
                                                         fis+5
                                                                   2 5    2 +    fi 3
                                                                                  2
                                                                                            2 s 2
                                                                                           s+S
                                                     =__L          s+S
                                                         .[2     s2 + 25
(b)                                                                              t<O
                                        =    0.03(1 - cos 2t)                    t 2: 0
                F2(s)     = /;     [f2(t)]       =   0.03   _l_ -        0.03        S      =     0.12
                                     ·                         s                s2 + 22         s(s2 + 4)
      --------------�--------------------------------------�------------
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