ME 391 Homework 4
Assigned: Mar 14, 2012
Due: Mar21, 2012
Problem 1: Using the Method of Undetermined Coefficients solve:
(5 pts)
= sin2x
ptox•e4*
1)
M’—i~2~ ~ø
2.
2.)C
t
U’
A~w~2-x
C
C
‘i
zszx-zes~~ix
-4~3~~ax —‘t6acsZx
1K- 4~c~ts&)
&j~i~~Zc
-
-at
4-2~M 4dnZx
tos 74-- 91
I,
--3,,
-4-- 2.0
~-‘Zc)
c.1e
‘C
Lx
k-C~e
-
3,
k&ez2.~)
Problem 2: Using the Variation of Parameters, solve: y”
(5 pts)
iL~
e
jietK
2y
=
e 3x
—I
I
to
-“I
W1zj
-c. ...j IJ
3x
C
cx
___
•e
~!
(4,
L
___
(.4~3
(Açz
-C
I
%jc
it
—
~:
I
I
—
-fr
___
4X
U&7y
-
,~
~
j\
3(4,
U4L.\1A_ct1u~
-~
~e (e
)A-
(a~
4x~
J•_3~c
Ce /
=
4
35<
a
~
3x
-~
4x
Problem 3: Using the substitution u
(5 pts)
(y÷l)y”=
L&:G~
6eparcic2.
=
y, solve the Differential Equation:
(y’)2
JLk
4~t~
\JoMna-L’.t~~
~
(~juj
La(~&~i+Ck
=)
LkCC~
ti.~zC~’
*
j~
(~I~4I) ~)cX~~
c-c
Problem 4: A 20-kg mass is attached to a spring. If the frequency of the simple
harmonic motion is 2 / tr cycles/s, what is the spring constant k? What is the frequency
of simple harmonic motion if the original mass is replaced with an 80-kg mass?
(5pts)
~
wtzW
2,
4/tr~uflt
I
~
I
l1,t’~i
e
tJ1
‘Wi
-~
2~
,~
L
—
Extra Credit: A mass of ¼ slug is attached to a spring having a spring constant of 1
lb/fl. The mass is started in motion by initially displacing it 2 ft. in the downward
direction and giving it an initial velocity of 2 ft/sec in the upward direction. Find the
equation of motion of the mass, if the force due to air resistance is -lxlb.
(5 pts)
~ ~f
°~f
sic
)( ~ ~4-~)c
frt~
~
~so~c
C
() x
Q,ti-~cJL\
i~~-~A
t6~4
~
—
~ xC~)
x
+zt& —U.
/ aA~~%d
tR
Vt~UCt~N