MATH 251 Exam 2 July 28, 2008 ANSWER KEY 1. 2. 3. B A (a) k = 8; (b) k = 4; (c) none (since there is nonzero damping, resonance could never happen); (d) T = . (a) f (t) = 2 + cos 2t sin 2t (b) f (t) = u3(t)(4e3t 9 cos(4t 12) + 4.5e3t 9 sin(4t 12) 5. f (t)
MATH 251
Exam II
April 2, 2013
ANSWER KEY (Form A)
1.
(a) True
2.
A
3.
B
4.
D
5.
A
6.
B
7.
C
8.
(b) True
(c) False
(d) True
8
1
(a) f (t ) = u10 (t ) e t 10 + e 2t + 20 4(t 10)e 2t + 20
3
3
t
t
(b) f (t ) = e cos 2t + e sin 2t 1 (t )
1 5 t 5 3t
1 1 t +
MATH 251
Exam II
April 3, 2012
ANSWER KEY (Form A)
1,
D
2.
B
3.
A
4.
D
5.
(a) 4u + 20u = 0
(c) = 200
(b) underdamped
(d) m = 2
6.
(a) F
(c) T
7.
4 cos 7t
4 sin 7t
+ C 2 e 5t
x(t ) = C1e 5t
5 cos 7t 6 sin 7t
6 cos 7t + 5 sin 7t
(b) T
8.
(a) f (t ) =
MATH 251 Exam II April 7, 2008 ANSWER KEY 1. 2, 3. 4. 5. 6. 7. A B D B B A
f (t ) = (1 u 5 (t ) ) ( t 2 ) + u 5 (t ) ( 4e 2 t )
F (s) =
s
4e 10 2 10 25 2 + e 5 s s + 2 + s3 + s2 + s s3
8.
1 1 t + 2 1 4 t 8 1 1 t + 6 1 4t 24 y (t ) = u 2 (t ) +e + e u
MATH 251 FALL SEMESTER 2013
Exam II study guide
Exam Date/Time: Tuesday, November 12, 6:30 to 7:45 pm
Format: 100 points in 14 questions (10 x multiple-choice, and 4 x partialcredit / short-answer)
Location: 101 Chambers (sections 1, 2); 26 Hosler (sectio
MATH 251
Name:
Examination II
November 13, 2012
Student Number:
FORM A
Section:
This exam has 12 questions for a total of 100 points. In order to obtain full credit for
partial credit problems, all work must be shown. For other problems, points might be
d
MATH 251 FALL SEMESTER 2013
Final Exam study guide
Exam Date/Time: Thursday, December 19, 2013, from 6:50 to 8:40 pm
Format: 150 points in 16 questions (incl. 11 multiple-choice questions). The exam is
cumulative, with approx. 62% based on new (chapter 10
MATH 251
Name:
Examination I
July 3, 2012
Student Number:
FORM A
Section:
This exam has 10 questions for a total of 100 points. Show all you your work! In order to obtain
full credit for partial credit problems, all work must be shown. Credit will not be
MATH 251
Exam II
November 13, 2012
ANSWER KEY
1.
Form A
A
Form B
D
2.
D
A
3.
C
A
4.
B
C
5.
A
C
6.
B
D
7.
D
C
8.
A
B
9.
10.
11.
12.
T, T, F, T, F
F, F, T, F, T
9 2t 5
9
e t
4
2
4
4 ( t 4 )
(b) f (t ) = u 4 (t )[e
cos 2(t 4) 2 e 4(t 4) sin 2(t 4)] 4 (t 7)
(
MATH 251
Exam II
July 25, 2011
ANSWER KEY
1.
y = C1 + C2 t + C3 t 2 + C4 e! t cos 2t + C5 e! t sin 2t
2.
#
!
x2
% x1 =
%
x3
$ x! =
2
%
!
% x3 = "4 x1 + 2 x2 " 3x3 + sin 2t
&
3.
(a) The integral represents the Laplace transform of f (t) = e4t cos 3t. There
MATH 251 FALL SEMESTER 2013
Exam I study guide
Exam Date/Time: Thursday, October 10, 6:30 to 7:45 pm
Format: 100 points in 13 questions (9 x multiple-choice, and 4 x partialcredit / short-answer)
Location: 108 Forum (sections 1, 5); 111 Forum (sections 2,
MATH 251
Name:
Examination II
July 25, 2011
Student Number:
FORM A
Section:
This exam has 10 questions for a total of 100 points. In order to obtain full credit for
partial credit problems, all work must be shown. For other problems, points might be
deduc