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Problem 2 (a): Match each ODE to its corresponding step response. All initial conditions are zero. ODE 4x+2x+4x=4u(t) Graph Step responses Graph 1 Graph 2 Graph 3 1 1 2 0.8 0.8 1.5 *+2x+100x = 100u(t) 0.6 0.6 1 0.4 0.4 2+8x+8x= 16u(t) 0.5 0.2 0.2 +5x+100x = 100u(t) 4x + x = u(t) Q 0 1 2 3 4 5 0 5 10 15 20 0 1 2 3 4 5 Graph 4 1.5 0.5 x + x = u(t) 1.5 0.5 Graph 5 Graph 6 1.5 0.5 0° 1 2 0 1 2 3 4 5 Ο 5 10 15 20

Problem 2 (a): Match each ODE to its corresponding step response. All initial conditions are zero. ODE 4x+2x+4x=4u(t) Graph Step responses Graph 1 Graph 2 Graph 3 1 1 2 0.8 0.8 1.5 *+2x+100x = 100u(t) 0.6 0.6 1 0.4 0.4 2+8x+8x= 16u(t) 0.5 0.2 0.2 +5x+100x = 100u(t) 4x + x = u(t) Q 0 1 2 3 4 5 0 5 10 15 20 0 1 2 3 4 5 Graph 4 1.5 0.5 x + x = u(t) 1.5 0.5 Graph 5 Graph 6 1.5 0.5 0° 1 2 0 1 2 3 4 5 Ο 5 10 15 20

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 2 (a): Match each ODE to its corresponding step response. All initial conditions are zero. ODE Graph Step responses 4x+2x+4x=4u(t) Graph 1 0.8 0.8 *+2x+100x = 100u(t) 0.6 0.6 0.4 0.4 2x+8x+8x=16u(t) 0.2 0.2 *+5x+100x = 100u(t) 4x+x= u(t) Graph 2 1.5 0.5 Graph 3 1 4 5 0 5 10 15 20 0 1 2 3 4 5 Graph 4 1.5 0.5 x+x= u(t) 1.5 0.5 Graph 5 Graph 6 1.5 0.5 1 2 1 2 3 4 5 5 10 15 20 Problem 2 (b): The poles (roots) of five linear systems are plotted below in the s-domain. Each system is indicated by a different marker (e.g., both triangle markers are for system iii). (a) What is the order of each system? Imaginary axis (rad/sec) 5 4 O(ii) 1 32- -2 -3 *(i) O A (iii) (iv) x x ㅁ A(v) (i) (ii) (iii) (iv) (v) (b) Which systems are stable? (i) (ii) (ii) (iv) (v) (b) Rank the stable systems in order of settling time ← Fastest Slowest → -4 -5 (d) Which 2nd-order system has the largest wn? -7 -6 -5 -4 -3 -2 -1 0 1 2 3 (e) Which 2nd-order system has the largest ?? Real axis (rad/sec)
Transcribed Image Text:Problem 2 (a): Match each ODE to its corresponding step response. All initial conditions are zero. ODE Graph Step responses 4x+2x+4x=4u(t) Graph 1 0.8 0.8 *+2x+100x = 100u(t) 0.6 0.6 0.4 0.4 2x+8x+8x=16u(t) 0.2 0.2 *+5x+100x = 100u(t) 4x+x= u(t) Graph 2 1.5 0.5 Graph 3 1 4 5 0 5 10 15 20 0 1 2 3 4 5 Graph 4 1.5 0.5 x+x= u(t) 1.5 0.5 Graph 5 Graph 6 1.5 0.5 1 2 1 2 3 4 5 5 10 15 20 Problem 2 (b): The poles (roots) of five linear systems are plotted below in the s-domain. Each system is indicated by a different marker (e.g., both triangle markers are for system iii). (a) What is the order of each system? Imaginary axis (rad/sec) 5 4 O(ii) 1 32- -2 -3 *(i) O A (iii) (iv) x x ㅁ A(v) (i) (ii) (iii) (iv) (v) (b) Which systems are stable? (i) (ii) (ii) (iv) (v) (b) Rank the stable systems in order of settling time ← Fastest Slowest → -4 -5 (d) Which 2nd-order system has the largest wn? -7 -6 -5 -4 -3 -2 -1 0 1 2 3 (e) Which 2nd-order system has the largest ?? Real axis (rad/sec)
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