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2. An input function is called doublet pulse as shown in the figure. (a) Find the Laplace transform of this function (b) What is the response of a process having a first-order transfer function K/(ts + 1) to this input? Draw the dynamic response. (c) What is the response of an integrating process K/s to this input? Draw the dynamic response. xDp (t) h 0 -h tw 2tw t

2. An input function is called doublet pulse as shown in the figure. (a) Find the Laplace transform of this function (b) What is the response of a process having a first-order transfer function K/(ts + 1) to this input? Draw the dynamic response. (c) What is the response of an integrating process K/s to this input? Draw the dynamic response. xDp (t) h 0 -h tw 2tw t

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 Statement 2. An input function is called a doublet pulse as shown in the figure. (a) Find the Laplace transform of this function. (b) What is the response of a process having a first-order transfer function \( \frac{K}{(\tau s + 1)} \) to this input? Draw the dynamic response. (c) What is the response of an integrating process \( \frac{K}{s} \) to this input? Draw the dynamic response. ## Diagram Explanation ### Doublet Pulse Function \( x_{DP}(t) \) - **Graph Description:** - The graph is a time-domain representation of a doublet pulse function. - The graph is composed of two rectangular pulses: - The first pulse has a height of \( h \) and lasts from time \( 0 \) to \( t_w \). - The second pulse has a height of \( -h \) and lasts from \( t_w \) to \( 2t_w \). - The horizontal axis is labeled \( t \), representing time. - The vertical axis is labeled \( x_{DP}(t) \), representing the function’s amplitude. - **Graph Characteristics:** - Positive pulse starts at \( t = 0 \) and ends at \( t = t_w \). - Negative pulse starts at \( t = t_w \) and ends at \( t = 2t_w \). - The pulse heights are equal in magnitude but opposite in direction.
Transcribed Image Text:## Problem Statement 2. An input function is called a doublet pulse as shown in the figure. (a) Find the Laplace transform of this function. (b) What is the response of a process having a first-order transfer function \( \frac{K}{(\tau s + 1)} \) to this input? Draw the dynamic response. (c) What is the response of an integrating process \( \frac{K}{s} \) to this input? Draw the dynamic response. ## Diagram Explanation ### Doublet Pulse Function \( x_{DP}(t) \) - **Graph Description:** - The graph is a time-domain representation of a doublet pulse function. - The graph is composed of two rectangular pulses: - The first pulse has a height of \( h \) and lasts from time \( 0 \) to \( t_w \). - The second pulse has a height of \( -h \) and lasts from \( t_w \) to \( 2t_w \). - The horizontal axis is labeled \( t \), representing time. - The vertical axis is labeled \( x_{DP}(t) \), representing the function’s amplitude. - **Graph Characteristics:** - Positive pulse starts at \( t = 0 \) and ends at \( t = t_w \). - Negative pulse starts at \( t = t_w \) and ends at \( t = 2t_w \). - The pulse heights are equal in magnitude but opposite in direction.
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