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MIME3380 Hwk 1: solution 9/12/2011 ________________________________________________________________________ 1 2 i 1.   0.5  0.866i 3   0.25  0.25i (  1  i)  0.794  0.794i  2  2 i 1  i 3 i 5 2i

2.

5i( 2  i)

10i  5

( 2  i) ( 2  i)

4 1

2

3.

( 1  i)  ( 1  i)  5  6  3i

4.

t e

 2t

1 ( s  2)

5.

 1  2i

 

3sin 5t 

a

2

  (t) 4

   (t)  3 cos( 5t) sin   (t)  4  4    (t) 3 sin(5t) cos Laplace transform of 4 3 sin(5t) cos

Laplace transform of

is



15  2



2

2 s  25

3  2 s

   (t) 4 

3 cos( 5t) sin

is

Putting everything together, the Laplace transform becomes:

2

2 s  25



 s  5  2 2

3 2  2

s  25 0.03( 1  cos(2t) )  (t)

b

0.03 (t)  0.03cos( 2 t)  (t) 0.03

The Laplace transform becomes: 6.

2   t

t e

Laplace transform:

s 2

(   s)

3

s  0.03 2 s 4...