Applied Statics and Strength of Materials (6th Edition)
6th Edition
ISBN: 9780133840544
Author: George F. Limbrunner, Craig D'Allaird, Leonard Spiegel
Publisher: PEARSON
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Chapter 7, Problem 7.11P
Locate the X-X and Y-Y centroidal axes for the areas shown.
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Example-1:
l
D
A uniform rotor of length 0.6 m and diameter 0.4 m is made of steel (density 7810 kg/m³)
is supported by identical short bearings of stiffness 1 MN/m in the horizontal and vertical
directions. If the distance between the bearings is 0.7 m, determine the natural frequencies
and plot whirl speed map.
Solution:
B
find the laplace transform for the
flowing function
2(1-e)
Ans. F(s)=-
S
12)
k
0
Ans. F(s)=
k
s(1+e)
0 a
2a 3a 4a
13)
2+
Ans. F(s)=
1
s(1+e")
3
14) f(t)=1, 0
Find the solution of the following Differential Equations
Using Laplace Transforms
1) 4y+2y=0.
y(0)=2.
y'(0)=0.
2) y+w²y=0,
(0)=A,
y'(0)=B.
3) +2y-8y 0.
y(0)=1.
y'(0)-8.
4)-2-3y=0,
y(0)=1.
y'(0)=7.
5) y-ky'=0,
y(0)=2,
y'(0)=k.
6) y+ky'-2k²y=0,
y(0)=2,
y'(0) = 2k.
7) '+4y=0,
y(0)=2.8
8) y+y=17 sin(21),
y(0)=-1.
9) y-y-6y=0,
y(0)=6,
y'(0)=13.
10) y=0.
y(0)=4,
y' (0)=0.
11) -4y+4y-0,
y(0)=2.1.
y'(0)=3.9
12) y+2y'+2y=0,
y(0)=1,
y'(0)=-3.
13) +7y+12y=21e".
y(0)=3.5.
y'(0)=-10.
14) "+9y=10e".
y(0)=0,
y'(0)=0.
15) +3y+2.25y=91' +64.
y(0)=1.
y'(0) = 31.5
16)
-6y+5y-29 cos(2t).
y(0)=3.2,
y'(0)=6.2
17) y+2y+2y=0,
y(0)=0.
y'(0)=1.
18) y+2y+17y=0,
y(0)=0.
y'(0)=12.
19) y"-4y+5y=0,
y(0)=1,
y'(0)=2.
20) 9y-6y+y=0,
(0)-3,
y'(0)=1.
21) -2y+10y=0,
y(0)=3,
y'(0)=3.
22) 4y-4y+37y=0,
y(0)=3.
y'(0)=1.5
23) 4y-8y+5y=0,
y(0)=0,
y'(0)=1.
24)
++1.25y-0,
y(0)=1,
y'(0)=-0.5
25) y 2 cos(r).
y(0)=2.
y'(0) = 0.
26)
-4y+3y-0,
y(0)=3,
y(0) 7.
27) y+2y+y=e
y(0)=0.
y'(0)=0.
28) y+2y-3y=10sinh(27),
y(0)=0.
y'(0)=4.
29)…
Chapter 7 Solutions
Applied Statics and Strength of Materials (6th Edition)
Ch. 7 - A cylindrical cast-iron casting has an axial bole...Ch. 7 - Locate the center of gravity of the cast-iron...Ch. 7 - A 5-in.-diameter steel sphere is rigidly attached...Ch. 7 - A solid steel shaft is fabricated as shown. Locate...Ch. 7 - A wood mallet has a cylindrical head 6 in. long...Ch. 7 - The built-up member shown is composed of two...Ch. 7 - A concrete member has a cross section as shown....Ch. 7 - A thin steel plate, having the dimensions shown,...Ch. 7 - The U-shaped built-up section shown is composed of...Ch. 7 - Locate the centroid of the area shown. In part...
Ch. 7 - Locate the X-X and Y-Y centroidal axes for the...Ch. 7 - A built-up steel member is composed of a W1871...Ch. 7 - Locate the X-X and Y-Y centroidal axes for the...Ch. 7 - Find the center of gravity for the three-axle...Ch. 7 - For the following computer problems, any...Ch. 7 - For the following computer problems, any...Ch. 7 - For the following computer problems, any...Ch. 7 - A 2.in,-diameler hole, 5 in. long, is drilled into...Ch. 7 - Locate the center of gravity of the cube in...Ch. 7 - The head of a maul is made of steel d is 3 in. in...Ch. 7 - Locate the X-X centroidal axes for the cross...Ch. 7 - A built-up steel member is composed of a W2162...Ch. 7 - Locate the X-X centroidal axes for the cross...Ch. 7 - Locate the X-X and Y-Y centroidal axes for the...Ch. 7 - Locate the X-X and Y-Y centroidal axes for the...Ch. 7 - For the area shown, the X-X centroidal axis is...Ch. 7 - Locate the X-X and Y-Y centroidal axes for the...Ch. 7 - Locate the X-X and Y-Y centroidal axes for the...
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