Assignment #15
ECSE2410 Signals & Systems  Spring 2007
Fri 03/30/07
1(28).
Find the Laplace transform of
(a)(8)
.
⎩
⎨
⎧
else
0
3
<
t
<
1
1
=
(t)
x
a
(b)(10)
.
3)

u(t
e
=
(t)
x
2)

(t
b
(c)(10)
.
u(t)
)
45
+
t
(
e
5
=
(t)
x
t
2
c
°
π
cos
2(30). Find the
inverse
Laplace transform for the signals below.
Note. You must use properties.
No
integration is possible.
(a) (10) Find
x
a
(
t
) , the inverse Laplace transform of
s
e
s
X
s
a
+
−
=
−
1
1
)
(
2
.
(b) (10) Find
x
b
(
t
), the inverse Laplace transform of
)
4
+
s
(
s
1
+
2s

s
=
(s)
X
2
2
b
.
(c) (10)
Find
x
c
(
t
) , the inverse Laplace transform of
=
(s)
X
c
6
5
4
+
−
s
+
s
e
s
2
s
.
3(15).
Given the transfer function,
s)
+
(
s
+
s
10
=
H(s)
1
)
16
(
2
+
, find the impulse response.
4(15).
A secondorder system is described by the differential equation
)
(
)
(
)
(
2
)
(
2
2
t
x
t
y
dt
t
dy
dt
t
y
d
K
=
+
+
, where
K
is a constant.
(a) (5 pts) Find the value of
K
that will make the system critically damped.
(b) (5 pts) If
K
= 4, find the impulse response,
( )
t
h
, for this system.
(c) (5 pts) If
K
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