D1.22 For the following systems with outputs y and inputs r, find the transfer functions: (a) +3 +7y = 6r, + 5r2 – 45 dra dr? dt Ans. T1(s) = 6/(s² + 3s +7); Tj2(s) = (-4s+5)/(s² + 3s +7) (b) dyi +2yı = dt dr - 3r di di? dyz dr + 6y = 4 di dt Ans. T1(s) = (s – 3)/(s² +6s +2); T1(8) = 45/(s +6) (c) +6 dt d²r dr? + 3ri +72 + yi = d³y; +6 di drz + 2 = 4 dt dr Ans. T1(s) = (s³+3)/(s³ +7s² +6s + 1); T2(s) = 1/(s³ + 7s² + 6s + 1); T1(s) = 0; Tz(s) = 4s/(s³ +7s² + 6s + 1)
D1.22 For the following systems with outputs y and inputs r, find the transfer functions: (a) +3 +7y = 6r, + 5r2 – 45 dra dr? dt Ans. T1(s) = 6/(s² + 3s +7); Tj2(s) = (-4s+5)/(s² + 3s +7) (b) dyi +2yı = dt dr - 3r di di? dyz dr + 6y = 4 di dt Ans. T1(s) = (s – 3)/(s² +6s +2); T1(8) = 45/(s +6) (c) +6 dt d²r dr? + 3ri +72 + yi = d³y; +6 di drz + 2 = 4 dt dr Ans. T1(s) = (s³+3)/(s³ +7s² +6s + 1); T2(s) = 1/(s³ + 7s² + 6s + 1); T1(s) = 0; Tz(s) = 4s/(s³ +7s² + 6s + 1)
Introductory Circuit Analysis (13th Edition)
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ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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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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