EBK NUMERICAL METHODS FOR ENGINEERS
7th Edition
ISBN: 8220100254147
Author: Chapra
Publisher: MCG
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Textbook Question
Chapter 9, Problem 11P
Given the equations
(a) Solve by Gauss elimination with partial pivoting. Show all steps of the computation.
(b) Substitute your results into the original equations to check your answers.
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find the laplace transform for the
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S
12)
k
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0 a
2a 3a 4a
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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)…
Auto Controls
A union feedback control system has the following open loop transfer function
where k>0 is a variable proportional gain
i. for K = 1 , derive the exact magnitude and phase expressions of G(jw).
ii) for K = 1 , identify the gaincross-over frequency (Wgc) [where IG(jo))| 1] and phase cross-overfrequency [where <G(jw) = - 180]. You can use MATLAB command "margin" to obtain there quantities.
iii) Calculate gain margin (in dB) and phase margin (in degrees) ·State whether the closed-loop is stable for K = 1 and briefly justify your answer based on the margin . (Gain marginPhase margin)
iv. what happens to the gain margin and Phase margin when you increase the value of K?you
You can use for loop in MATLAB to check that.Helpful matlab commands : if, bode, margin, rlocus
NO COPIED SOLUTIONS
Chapter 9 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
Ch. 9 - (a) Write the following set of equations in matrix...Ch. 9 - A number of matrices are defined as...Ch. 9 - Three matrices are defined as...Ch. 9 - Use the graphical method to solve...Ch. 9 - 9.5 Given the system of equations
(a) Solve...Ch. 9 - 9.6 For the set of equations
(a) Compute the...Ch. 9 - Given the equations 0.5x1x2=9.51.02x12x2=18.8 (a)...Ch. 9 - Given the equations...Ch. 9 - Use Gauss elimination to solve:...Ch. 9 - Given the system of equations...
Ch. 9 - 9.11 Given the equations
(a) Solve by Gauss...Ch. 9 - Use Gauss-Jordan elimination to solve:...Ch. 9 - 9.13 Solve:
with (a) naive Gauss elimination,...Ch. 9 - 9.14 Perform the same computation as in Example...Ch. 9 - 9.15 Solve
Ch. 9 - 9.16 Develop, debug, and test a program in either...Ch. 9 - Develop, debug, and test a program in either a...Ch. 9 - Develop, debug, and test a program in either a...Ch. 9 - 9.19 Three masses are suspended vertically by a...Ch. 9 - 9.20 Develop, debug, and test a program in either...Ch. 9 - 9.21 Recall from Sec. 8.2 that determining the...
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