ESE 351 Quiz 1 Name: 9/2/2010
Sections 1.11.3 a. What state variable do you need to define if you see a mass in a mechanical system?
b. Let v denote the velocity of a mass M and its reference direction points to the right. This means that the mass is mov
ESE 351
Section 01 Spring 2013
Final Exam
5/8/2013
Name: _
Closed book and notes except for three personally created lettersize crib sheets with two sides.
Extra paper is available upon request.
The problems are approximately ordered in increasing diffic
ESE 351 Section 01 Spring 2013 2/12/2013
Test 2 Name: (Leer/Ca.
Closed book and notes except for one personally created lettersize crib sheet with two sides. No
calculators are allowed. Identify your answer clearly at the bottom ofeach page.
1. [7 points
ESE 351
Section 01 Spring 2013
Midterm Exam
3/5/2013
Name: _
Closed book and notes except for two personally created lettersize crib sheets with two sides. No
calculators are allowed. Identify your answers clearly at the bottom of each page. Use timedom
ESE 351 Section 01 Spring 2014 2/11/2014
TeStZ Name:
Closed book and notes except for one personally created lettersize crib sheet with two sides. N o
calculators are allowed. Identify your answer clearly at the bottom of each page.
1. [7 points] Consid
ESE 351
Section 01 Spring 2013
Final Exam
5/8/2013
Name: _
Closed book and notes except for three personally created lettersize crib sheets with two sides.
Extra paper is available upon request.
The problems are approximately ordered in increasing diffic
ESE 351 Signals and Systems
Fall 2016
Instructor: Randall Brown
Lecturer, Department of Electrical and Systems Engineering
Office: 2153 Green Hall
Email: [email protected]
Office Hours:
Mon 122
Fri
24
or by appointment.
Do not hesitate to request an
ESE 351 Fa16 Schedule
AUG
30
Lec 1: Read Ch 1
HW 1 on Blackboard
1.X Due F Sep 2 by 11:59 pm
SEP
6
Lec 3: Read Ch 1
HW 2 on Blackboard
13
Lec 5: Read Ch 2, Ch 3
End Exam 1 material
Read Ch 3
HW 3, 2.Y, 3.X on Blackboard
2.Y, 3.X Due F Sep 16 by 11:59 pm
2
Solution Set 11
11.1
Problem 11.7.2
See Figure 11.1.
+
G
u
y
C

Figure 11.1: A simple electrical system.
dy
+ Gy = u CsY + GY = U
dt
1
1
(b) Y (s) =
U H(s) =
Cs + G
Cs + G
1
(c) H(s) =
10s + 1
(a) C
u(t) =
U (s) =
Y (s) =
cos(t + )1(t) = cfw_cos t cos si
Solution Set 12
12.1
Problem 12.13.3 (a)
f (t)
0
10
t
Figure 12.1: A rectangular pulse.
(1) See Figure 12.1.
[
]10
1
1
eit dt = eit
= (ei10 1)
i
i
0
0
i5
i5
(e
e
)
10
1
(1 ei10 ) = ei5
= 10 sinc(5)ei5 .
i
2i
5
F ()
=
=
f (t)eit dt =
10
(2) Let g(t) = puls
Solution Set 4
4.1
Problem 4.9.2 (b)
The righthand side,
g(t) = (1) (t) + 10 (t) + 25 1(t),
is in the same class as (1) (t), because (1) (t) is the most singular. It follows that the leading term D2 y
is in the same class: D2 y (1) . Hence, Dy , y 1 and
Solution Set 13
13.1
Problem 13.9.2
See Figure 13.1 for the Fourier spectrum U () of the input signal u(t). We note that the its frequency
components range from 0 to m and its bandwidth is thus m .
U ( )
U (0 )
m m
0
m
m
Figure 13.1: Fourier spectrum U (
Solution Set 10
10.1
Problem 10.9.1
(a) T = 1, f (t) = 1 t, 0 t T .
1
2n
1 T
f (t)ei T t dt =
(1 t)ei2nt dt
T 0
0
cfw_ 1
]1
[
(1 t)dt = t 21 t2 0 = 12 ,
n = 0;
0
=
1 i2nt
1 i2nt
i
e
dt 0 te
dt = 2n , n =
0,
0
F (n) =
where ei2n = 1 for an integer n an
Solution Set 5
5.1
Problem 5.6.1
u 0 (t )
y 0 (t )
1
0
1
2
3
u 0 (t 1)
1
2
3
t
0
t
t
1
2
3
1
2
3
4
2
3
4
t
y 0 ( t 1)
1
u 0 (t 2 )
0
y 0 (t 2 )
2
3
4
5
t
2[u0 (t ) +
u0 (t 1) +
+ u0 (t 2)]
0
2
2
2[ y 0 ( t ) y 0 ( t 1) + y 0 ( t 2 )]
t
4
0
1
2
3
4
5
Fi
Solution Set 9
9.1
Problem 9.12.3 (b)
(i) Since the system eigenvalues are 1 = 1, 2 = 6 and 3 = 3, the system real mode functions
are et , e3t and e6t .
(ii) The transfer function H(s) has poles at s1 = 1, s2 = 3 and s3 = 6. The real mode functions
of H(s
Solution Set 3
2.1
Problem 3.6.2 (b)
The characteristic polynomial is
P (S) = 16 + 8S 1 + S 2 P () = (162 + 8 + 1)2 .
So the roots are 1 = 41 twice: 1 = 2. The general solution is
(
y(k) = C11
1
4
)k
(
1
+ C12 k
4
)k
.
The initial conditions yield
y(0) =
ESE 351 Section 01 Spring 2014 4/22/2014
Test 6 Name: rat/1,!
Closed book and notes except for one personally created lettersize crib sheet with two sides. No
calculators are allowed. Identify your answer clearly at the bottom of each page or wherever in
ESE 351 Section 01 Spring 2014 3/25/2014
Test 4 Name: a 2154
Closed book and notes except for one personally created lettersize crib sheet with two sides. N o
calculators are allowed. Identify your answer clearly at the bottom of each page or wherever in
ESE 351 Quiz 13 Name: 10/21/10
Sections 8.18.7 a. What is the inverse Laplace transform of (sI  A)1 if A is a square matrix? We are going back to a positive time function. Hint: Do you know the inverse Laplace transform of
1 s
if is a scalar?
b. What i