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Problem. Transfer function. Inverse Laplace with distinct and repeated poles. IVT and F A system with input x and output y is characterized by the differential equation: ÿ+ ÿ = x Y(s) a) Obtain the system transfer function H(s)= %3D X (s) b) Obtain the system impulse response h(t). Verify the values h(0* ) and h() by using the Initial Value Theorem (IVT) and the Final Value Theorem (FVT). c) Obtain the system step response by two different approaches: 1) Using the TF and PFE with repeated poles. 2) By integrating the impulse response. Why would approach 2) work?

Problem. Transfer function. Inverse Laplace with distinct and repeated poles. IVT and F A system with input x and output y is characterized by the differential equation: ÿ+ ÿ = x Y(s) a) Obtain the system transfer function H(s)= %3D X (s) b) Obtain the system impulse response h(t). Verify the values h(0* ) and h() by using the Initial Value Theorem (IVT) and the Final Value Theorem (FVT). c) Obtain the system step response by two different approaches: 1) Using the TF and PFE with repeated poles. 2) By integrating the impulse response. Why would approach 2) work?

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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**Problem: Transfer function. Inverse Laplace with distinct and repeated poles. IVT and FVT** A system with input \( x \) and output \( y \) is characterized by the differential equation: \[ \ddot{y} + \dot{y} = x \] a) Obtain the system transfer function \( H(s) = \frac{Y(s)}{X(s)} \) b) Obtain the system impulse response \( h(t) \). Verify the values \( h(0^+) \) and \( h(\infty) \) by using the Initial Value Theorem (IVT) and the Final Value Theorem (FVT). c) Obtain the system step response by two different approaches: 1) Using the TF and PFE with repeated poles. 2) By integrating the impulse response. Why would approach 2) work?
Transcribed Image Text:**Problem: Transfer function. Inverse Laplace with distinct and repeated poles. IVT and FVT** A system with input \( x \) and output \( y \) is characterized by the differential equation: \[ \ddot{y} + \dot{y} = x \] a) Obtain the system transfer function \( H(s) = \frac{Y(s)}{X(s)} \) b) Obtain the system impulse response \( h(t) \). Verify the values \( h(0^+) \) and \( h(\infty) \) by using the Initial Value Theorem (IVT) and the Final Value Theorem (FVT). c) Obtain the system step response by two different approaches: 1) Using the TF and PFE with repeated poles. 2) By integrating the impulse response. Why would approach 2) work?
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