D1.22 For the following systems with outputs y and inputs r, find the transfer functions: (a) drz +7y= 6r1 +5r2 – 4 dt dt Ans. T1(1s) = 6/(s² + 3s +7); Tj2(s) = (-4s+5)/(s² + 3s + 7) (b) dyi dr +6 +2yı = 3r dt? dt dr dt di |dyz - 62 = 4: dt Ans. T(8) = (s - 3)/(s² + 6s +2); Tz1(s) = 4s/(s +6) (c) d’y + + +» = dy d²r dt3 dt dr? + 3rı +r2 +7- di? +62 + = 4 drz dt dt Ans. T1(s) = (s³+ 3)/(s³ +7s² +6s + 1); T12(s) = 1/(s³ + 7s² + 6s + 1); T21 (s) = 0; T2(s) = 4s/(s³ + 7s² + 6s + 1) %3D
D1.22 For the following systems with outputs y and inputs r, find the transfer functions: (a) drz +7y= 6r1 +5r2 – 4 dt dt Ans. T1(1s) = 6/(s² + 3s +7); Tj2(s) = (-4s+5)/(s² + 3s + 7) (b) dyi dr +6 +2yı = 3r dt? dt dr dt di |dyz - 62 = 4: dt Ans. T(8) = (s - 3)/(s² + 6s +2); Tz1(s) = 4s/(s +6) (c) d’y + + +» = dy d²r dt3 dt dr? + 3rı +r2 +7- di? +62 + = 4 drz dt dt Ans. T1(s) = (s³+ 3)/(s³ +7s² +6s + 1); T12(s) = 1/(s³ + 7s² + 6s + 1); T21 (s) = 0; T2(s) = 4s/(s³ + 7s² + 6s + 1) %3D
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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plz provide step by step answer for question 1.21 asap
Transcribed Image Text:D1.22 For the following systems with outputs y and inputs r, find the transfer
functions:
(a)
d²y
dr?
drz
+32 +7y = 6rı + 5r2 - 4
dt
dt
Ans. T1(s) = 6/(s² + 3s + 7); T12(s) = (-4s +5)/(s² + 3s + 7)
d²y,
dy
+6-
dt?
dr
+2yı
3r
%3D
dt
dt
dyz
+ 6y2 = 4
dt
dr
dt
Ans. T1(s) = (s - 3)/(s² +6s +2); T1(s) = 4s/(s +6)
%3D
ww.
(c)
d?ri
di?
di3
dr2
+6-
dt
+ yı =
+ 3rı +r2
dy2
dr2
+ y2 = 4-
dr
+7
+6
dr3
dt?
dt
Ans. T1(s) = (s³ + 3)/(s +7s² + 6s + 1);
T12(s) = 1/(s³ + 7s² + 6s + 1);
T21 (s) = 0;
T2(s) = 4s/(s³ + 7s² + 6s + 1)
%3D
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