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Part 1: Problem 4B Match the transfer function shown in the left column by place the correct letter next to the right column showing the correct response showing the basic response to a step input.

Part 1: Problem 4B Match the transfer function shown in the left column by place the correct letter next to the right column showing the correct response showing the basic response to a step input.

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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**Part 1: Problem 4B** **Task:** Match the transfer function shown in the left column by placing the correct letter next to the right column, showing the correct response indicating the basic response to a step input. **Hint:** Look at Zeta for each function, and determine the state of response (Underdamped, overdamped, critically damped, or Zero Damp, which means oscillation continuously). --- **Problem:** For each of the following transfer functions, by inspection, write the general form of the step response: a. \( G(s) = \frac{400}{s^2 + 12s + 400} \) b. \( G(s) = \frac{900}{s^2 + 90s + 900} \) c. \( G(s) = \frac{225}{s^2 + 30s + 225} \) d. \( G(s) = \frac{625}{s^2 + 625} \) **Options for step response:** 1. \( c(t) = A + Be^{-6t} \cos(19.08t + \phi) \) 2. \( c(t) = A + Be^{-78.54t} + Ce^{-11.46t} \) 3. \( c(t) = A + Be^{-15t} + Ct e^{-15t} \) 4. \( c(t) = A + B \cos(25t + \phi) \) Place the correct response next to each function by analyzing its characteristics.
Transcribed Image Text:**Part 1: Problem 4B** **Task:** Match the transfer function shown in the left column by placing the correct letter next to the right column, showing the correct response indicating the basic response to a step input. **Hint:** Look at Zeta for each function, and determine the state of response (Underdamped, overdamped, critically damped, or Zero Damp, which means oscillation continuously). --- **Problem:** For each of the following transfer functions, by inspection, write the general form of the step response: a. \( G(s) = \frac{400}{s^2 + 12s + 400} \) b. \( G(s) = \frac{900}{s^2 + 90s + 900} \) c. \( G(s) = \frac{225}{s^2 + 30s + 225} \) d. \( G(s) = \frac{625}{s^2 + 625} \) **Options for step response:** 1. \( c(t) = A + Be^{-6t} \cos(19.08t + \phi) \) 2. \( c(t) = A + Be^{-78.54t} + Ce^{-11.46t} \) 3. \( c(t) = A + Be^{-15t} + Ct e^{-15t} \) 4. \( c(t) = A + B \cos(25t + \phi) \) Place the correct response next to each function by analyzing its characteristics.
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