This preview shows pages 1–2. Sign up to view the full content.
1
EE102 Spring 200910
Lee
Systems and Signals
Homework #7
Due: Tuesday, June 1, 2010 5PM
1. Find the Laplace transform of the following signals:
(a)
f
(
t
) = (1

t
2
)
e

2
t
.
(b) One cycle of a sinusoid,
f
(
t
)=
±
sin(2
πt
)0
≤
t<
1
01
≤
t
which is plotted below:
0
1
2
t
f
(
t
)
1

1
Hint:
Use the delay theorem, and the fact that a delayed signal is padded with zeros.
(c) Find the Laplace transform of the following signal,
t
t
2
1
1
0
2
3
4
5
f
(
t
)
Hint:
Differentiate once or twice, and then use the integral theorem.
(d) Find the Laplace transform of the following signal
t
1
2
0
3
f
(
t
)
e

t
1
This is a cosine with an envelope that bounds the cosine below by
0
and above by
e

t
.
Combine terms over a common denominator, and simplify your answer.
Hint:
Express the signal as a sum of a decaying exponential, and an exponentially
decaying cosine.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document2
2. Find the Inverse Laplace transforms of the following functions
(a)
4
s
3
+4
s
(b)
s
+3
(
s
+ 1)
2
(
s
+ 2)
(c)
10
(
s
+ 1)(
s
2
s
+ 13)
(d)
s
2
+8
s
s
2
s
+ 25
3.
Solving Differential Equations
A system is described by the differential equation
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '09
 Levan

Click to edit the document details