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A system is represented by the following ordinary differential equation: d²y(t) dt2 dy(t) +3 +2y(t) =x(t) dt where y(t) is the system output and x(t) is the input. (a) Find the transfer function H (s) = Y (s)/ X (s) of the system. From its poles and zeros de- termine if the system is BIBO stable or not. (b) If x (t) = u(t), and initial conditions are zero, determine the steady-state response yss (t). What if the initial conditions were not zero, would you get the same steady state? Explain. Answers: H(s) = 1/(s² +3s + 2); BIBO stable; yss (t) = 0.5.

A system is represented by the following ordinary differential equation: d²y(t) dt2 dy(t) +3 +2y(t) =x(t) dt where y(t) is the system output and x(t) is the input. (a) Find the transfer function H (s) = Y (s)/ X (s) of the system. From its poles and zeros de- termine if the system is BIBO stable or not. (b) If x (t) = u(t), and initial conditions are zero, determine the steady-state response yss (t). What if the initial conditions were not zero, would you get the same steady state? Explain. Answers: H(s) = 1/(s² +3s + 2); BIBO stable; yss (t) = 0.5.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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3.7 A system is represented by the following ordinary differential equation: d²y(t) dy(t) +3 +2y(t) = x(t) dt2 dt where y(t) is the system output and x(t) is the input. (a) Find the transfer function H (s) = Y (s)/ X (s) of the system. From its poles and zeros de- termine if the system is BIB0 stable or not. (b) If x(t) = u (1), and initial conditions are zero, determine the steady-state response yss(t). What if the initial conditions were not zero, would you get the same steady state? Explain. Answers: H(s) = 1/(s² + 3s + 2); BIBO stable; yss (t) = 0.5.
Transcribed Image Text:3.7 A system is represented by the following ordinary differential equation: d²y(t) dy(t) +3 +2y(t) = x(t) dt2 dt where y(t) is the system output and x(t) is the input. (a) Find the transfer function H (s) = Y (s)/ X (s) of the system. From its poles and zeros de- termine if the system is BIB0 stable or not. (b) If x(t) = u (1), and initial conditions are zero, determine the steady-state response yss(t). What if the initial conditions were not zero, would you get the same steady state? Explain. Answers: H(s) = 1/(s² + 3s + 2); BIBO stable; yss (t) = 0.5.
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