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Problem # 7A Part A: Show all your work. Identify the transfer function X{s)/F(s) from the block diagram shown in figure. [Set G/s) = 0.] G(s)| F(s) X(s) PAR TB: After your determine zeta and if the: critically damped, underda damp using any method yc X(s) F(s) 3-8s-24 a. Critically Over dampea X(s) F(s) s+8s+24 IF you select this problem (which I highly recommend, you must cross out the other problem b. Over Damped D X(s) F(s) s'+8s-24 c. Underdamped

Problem # 7A Part A: Show all your work. Identify the transfer function X{s)/F(s) from the block diagram shown in figure. [Set G/s) = 0.] G(s)| F(s) X(s) PAR TB: After your determine zeta and if the: critically damped, underda damp using any method yc X(s) F(s) 3-8s-24 a. Critically Over dampea X(s) F(s) s+8s+24 IF you select this problem (which I highly recommend, you must cross out the other problem b. Over Damped D X(s) F(s) s'+8s-24 c. Underdamped

Introduction to Chemical Engineering Thermodynamics
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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### Problem #7A **Part A: Show all your work.** Identify the transfer function \( \frac{X(s)}{F(s)} \) from the block diagram shown in the figure. [Set \( G(s)' = 0.\)] --- **Diagram Explanation:** The block diagram includes several elements connected in a feedback loop: - An input function \( F(s) \). - A block with gain 4. - A block with transfer function \( \frac{1}{s} \). - A summing junction that combines the outputs of previous blocks. - Another block with transfer function \( \frac{1}{s} \). - A feedback loop with gain 8 feeding back into the summing junction. - A feedback loop with gain 6 feeding back after the summing junction. --- **Options for Transfer Function:** 1. \( \frac{X(s)}{F(s)} = \frac{4}{s^2 - 8s - 24} \) 2. \( \frac{X(s)}{F(s)} = \frac{4}{s^2 + 8s + 24} \) 3. \( \frac{X(s)}{F(s)} = \frac{4}{s^2 + 8s - 24} \) 4. \( \frac{X(s)}{F(s)} = \frac{4}{s^2 - 8s + 24} \) --- **Note:** *IF you select this problem (which I highly recommend), you must cross out the other problem.* --- **Part B:** After your selection, determine the damping ratio (\( \zeta \)) and decide whether the response is critically damped, overdamped, underdamped, or not damped using any method you choose: a. Critically Overdamped b. Overdamped c. Underdamped d. Not Damped, Oscillates continuously ---
Transcribed Image Text:### Problem #7A **Part A: Show all your work.** Identify the transfer function \( \frac{X(s)}{F(s)} \) from the block diagram shown in the figure. [Set \( G(s)' = 0.\)] --- **Diagram Explanation:** The block diagram includes several elements connected in a feedback loop: - An input function \( F(s) \). - A block with gain 4. - A block with transfer function \( \frac{1}{s} \). - A summing junction that combines the outputs of previous blocks. - Another block with transfer function \( \frac{1}{s} \). - A feedback loop with gain 8 feeding back into the summing junction. - A feedback loop with gain 6 feeding back after the summing junction. --- **Options for Transfer Function:** 1. \( \frac{X(s)}{F(s)} = \frac{4}{s^2 - 8s - 24} \) 2. \( \frac{X(s)}{F(s)} = \frac{4}{s^2 + 8s + 24} \) 3. \( \frac{X(s)}{F(s)} = \frac{4}{s^2 + 8s - 24} \) 4. \( \frac{X(s)}{F(s)} = \frac{4}{s^2 - 8s + 24} \) --- **Note:** *IF you select this problem (which I highly recommend), you must cross out the other problem.* --- **Part B:** After your selection, determine the damping ratio (\( \zeta \)) and decide whether the response is critically damped, overdamped, underdamped, or not damped using any method you choose: a. Critically Overdamped b. Overdamped c. Underdamped d. Not Damped, Oscillates continuously ---
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