Engineering Mechanics - Statics, Eighth Edition Si Version
8th Edition
ISBN: 9781119044673
Author: Kraige, Bolton Meriam
Publisher: WILEY
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Chapter 1, Problem 3P
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find the laplace transform for the
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2(1-e)
Ans. F(s)=-
S
12)
k
0
Ans. F(s)=
k
s(1+e)
0 a
2a 3a 4a
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2+
Ans. F(s)=
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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)…
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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 1 Solutions
Engineering Mechanics - Statics, Eighth Edition Si Version
Ch. 1 - Determine the angles made by the vector V=36i+15j...Ch. 1 - Determine the magnitude of the vector sum V=V1+V2...Ch. 1 - For the given vectors V1 and V2 of Prob. 1/2,...Ch. 1 - A force is specified by the vector...Ch. 1 - What is the mass in both slugs and kilograms of a...Ch. 1 - From the gravitational law calculate the weight W...Ch. 1 - Determine the weight in newtons of a woman whose...Ch. 1 - Suppose that two nondimensional quantities are...Ch. 1 - Compute the magnitude F of the force which the sun...Ch. 1 - Determine the small gravitational force F which...
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- 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 SOLUTIONSarrow_forwardAuto Controls Hand sketch the root Focus of the following transfer function How many asymptotes are there ?what are the angles of the asymptotes?Does the system remain stable for all values of K NO COPIED SOLUTIONSarrow_forward-400" 150" in Datum 80" 90" -280"arrow_forward
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