Name ____________________________

ECE 350 – Quiz #2

September 28, 2011

Problem 1

Find f(t), the inverse Laplace transform of:

F(s) = 7s2 +30s+ 40

s3 +8s2 + 20s

----------------------------

F(s) = 7s2 +30s+ 40

s3 +8s2 + 20s=7s2 +30s+ 40s s2 +8s+ 20( )

=As+

Bs+Cs2 +8s+ 20

! A = 2,B = 5,C =14

F(s) = 2s+

5s+14s2 +8s+ 20

=2s+

5s+14s+ 4( )2 + 22

=2s+

5 s+ 4( )s+ 4( )2 + 22

+"3(2)

s+ 4( )2 + 22

f (t) = 2+ 5e"4t cos2t "3e"4t sin2t#$ %&u(t)

Problem 2

For the circuit shown below, i(0) = 1A and v(0) = 5V. Find I(s), the Laplace

transform of the current, i(t), t≥0. Do NOT find i(t).

---------------------------

Transform the circuit:

Writing KCL:

8 I(s)! 2s

"

#$%

&'+8sI(s)+ 5

s+ 2sI(s)! 2+ 3

s= 0

( I(s) = s+ 4s2 + 4s+ 4

+-­

+        v        -­

2A

1/8  Fi 2H

3V

+-­

+        v        -­

2/s

8/s 2s

3/s

+ -­

+-­I(s)5/s 2