The transfer function of a linear system is defined as the ratio of the Laplace transform of the output function y(t) to the Laplace transform of the input function g(t), when all initial conditions are zero. If a linear system is governed by the differential equation below, Y(s) for this system. use the linearity property of the Laplace transform and Theorem 5 to determine the transfer function H(s) = G(s) y'' (t) + 8y' (t) +9y(t) = g(t). t> 0 Click here to view Theorem 5 H(s) = Let f(t) f'(t)... -1) (t) be continuous on [0,∞) and let f(n) (t) be piecewise continous on [0,00), with all these functions of exponential order a. Then for s> a, the following equation holds true. L {f{")} (s) = s^L{f}(s) — s"~1¹f(0) -sª-²f'(0) --- (-¹) (0)
The transfer function of a linear system is defined as the ratio of the Laplace transform of the output function y(t) to the Laplace transform of the input function g(t), when all initial conditions are zero. If a linear system is governed by the differential equation below, Y(s) for this system. use the linearity property of the Laplace transform and Theorem 5 to determine the transfer function H(s) = G(s) y'' (t) + 8y' (t) +9y(t) = g(t). t> 0 Click here to view Theorem 5 H(s) = Let f(t) f'(t)... -1) (t) be continuous on [0,∞) and let f(n) (t) be piecewise continous on [0,00), with all these functions of exponential order a. Then for s> a, the following equation holds true. L {f{")} (s) = s^L{f}(s) — s"~1¹f(0) -sª-²f'(0) --- (-¹) (0)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:The transfer function of a linear system is defined as the ratio of the Laplace transform of the output function y(t) to the Laplace
transform of the input function g(t), when all initial conditions are zero. If a linear system is governed by the differential equation below,
Y(s)
for this system.
G(s)
use the linearity property of the Laplace transform and Theorem 5 to determine the transfer function H(s) =
y''(t) + 8y' (t) +9y(t) = g(t), t> 0
Click here to view Theorem 5.
H(s) =
Let f(t) f'(t),..., f(n-1) (t) be continuous on [0,00) and let f(n) (t) be piecewise
continous on [0,00), with all these functions of exponential order. Then for s> α,
the following equation holds true.
L {f(n)} (s) = s" L{f}(s) - s"-¹f(0) - s^-²f'(0) - ... -f(n − 1) (0)
aplo
hlp.
JA
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
