MATH 251
Examination II
April 4, 2011
FORM A
Name:
Student Number:
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
deducted, at the sole discretion of the instructor, for an answer not supported by a
reasonable amount of work.
The point value for each question is in parentheses to the right of
the question number. A table of Laplace transforms is attached as the last page of the exam.
Please turn off and put away your cell phone.
You may not use a calculator on this exam.
1:
2
thru
7:
8:
9:
10:
11:
12:
Total:
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MATH 251
EXAMINATION II
April 4, 2011
1. (12 points) A massspring system is described by the equation
4
u
00
+
γu
0
+
ku
=
F
(
t
)
.
(a) (3 points) Suppose the mass originally stretched the spring 2
m
to reach its equilibrium
position.
What is the spring constant
k
?
(Assume
g
= 10
m/s
2
to be the gravitational
constant.)
(b) (3 points) Suppose
k
= 25. For what value(s) of
γ
would this system be critically damped
?
(c) (3 points) Suppose
γ
= 0 and
k
= 400. What is the natural
period
of this system?
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 Spring '08
 CHEZHONGYUAN
 Math, Differential Equations, Equations, Partial Differential Equations, Laplace, Elementary algebra

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