CHAPTER 1

1. 1. L.I.

   2. L.I.

   3. L.I.

   4. L.D.

   5. L.I.

   6. L.D.

   7. L.I.

   8. L.I.

2. 1. u _h( t) = c ₁ e ^{-4 t} + c ₂ e ^{4 t}

   2. u _h( t) = c ₁ e ^t + c ₂ te ^t + c ₃ t ² e ^t

   3. u _h( t) = c ₁ + c ₂ t + c ₃ t ² + c ₄ t ³

   4. 

   5. u _h( t) = c ₁ e ^{-3 t} sin 4 t + c ₂ e ^{-3 t} cos 4 t

3. 1. a ? b,	k( t - ?) = [ e - a ( t - ? ) - e -b ( t - ? )]
      a = b,	k( t - ?) = ( t - ?) e -b ( t - ? )

   2. From (1.4-1),

4. From (1.4-1), v ₁( ?) = v ₂( ?) =

5. 1. From Problem 1-4,

   2. 

   3. From (1.8-3),

6. From (1.6-3)

   1. e ^-48

   2. e ^?

   3. 0

7. 
   Figure A.1-7

8. 1. k _t( t - ?) = e ^{-( R/L )( t - ? )}; h( t - ?) = u _-1( t - ?) k ₁( t - ?)

   2. 
      Figure A.1-8

   3. 

      General shape is shown in Fig. 1-5.

   4. 1. Response is that of (c) with T