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Problem 3 (restated for convenience): A causal system with input x(t) and output y(t) obeys the differential equation d²y dy dt² dt - 2y(t) = dx dt +3x(t) = 3(b) 10 points Assume that the output obeys the initial condition y(0) = 3, and the input is x(t) eu(t) as in 5(a). Can you find an initial condition for the derivative of the output, y'(0-), such that y(t) does not blow up as t gets large? If so, specify the value of the initial condition. If not, say why not. Zero input response 5(64(5) -4(0))-(0)-(sy (5) - 4(0))-2Y(=0 -ylo 5²-s-2) Y(St) = sy(o-) -y (σ`¯)+y' (0¯ ) Y(5) 2 35 - 3+ y' (0°) 35-3+4(0) (5-2) (5+1) A = B + 5-2 5+1 A = 6-3+y' (0-) = 1+5607/3 3 라 Need A = -1/3 to cancel out e²t term in zero state response | + 4 (0¯ ) = -1/2 =)) y ( 0 ) == 4 3

Problem 3 (restated for convenience): A causal system with input x(t) and output y(t) obeys the differential equation d²y dy dt² dt - 2y(t) = dx dt +3x(t) = 3(b) 10 points Assume that the output obeys the initial condition y(0) = 3, and the input is x(t) eu(t) as in 5(a). Can you find an initial condition for the derivative of the output, y'(0-), such that y(t) does not blow up as t gets large? If so, specify the value of the initial condition. If not, say why not. Zero input response 5(64(5) -4(0))-(0)-(sy (5) - 4(0))-2Y(=0 -ylo 5²-s-2) Y(St) = sy(o-) -y (σ`¯)+y' (0¯ ) Y(5) 2 35 - 3+ y' (0°) 35-3+4(0) (5-2) (5+1) A = B + 5-2 5+1 A = 6-3+y' (0-) = 1+5607/3 3 라 Need A = -1/3 to cancel out e²t term in zero state response | + 4 (0¯ ) = -1/2 =)) y ( 0 ) == 4 3

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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I understand the entire solution for this question except for the choice of setting A as -1/3 why do we need it to be -1/3? Could you explain how to solve this problem and detail the reason why we do each step?

Problem 3 (restated for convenience): A causal system with input x(t) and output y(t) obeys the differential equation d²y dy dt² dt - 2y(t) = dx dt +3x(t) = 3(b) 10 points Assume that the output obeys the initial condition y(0) = 3, and the input is x(t) eu(t) as in 5(a). Can you find an initial condition for the derivative of the output, y'(0-), such that y(t) does not blow up as t gets large? If so, specify the value of the initial condition. If not, say why not. Zero input response 5(64(5) -4(0))-(0)-(sy (5) - 4(0))-2Y(=0 -ylo 5²-s-2) Y(St) = sy(o-) -y (σ`¯)+y' (0¯ ) Y(5) 2 35 - 3+ y' (0°) 35-3+4(0) (5-2) (5+1) A = B + 5-2 5+1 A = 6-3+y' (0-) = 1+5607/3 3 라 Need A = -1/3 to cancel out e²t term in zero state response | + 4 (0¯ ) = -1/2 =)) y ( 0 ) == 4 3
Transcribed Image Text:Problem 3 (restated for convenience): A causal system with input x(t) and output y(t) obeys the differential equation d²y dy dt² dt - 2y(t) = dx dt +3x(t) = 3(b) 10 points Assume that the output obeys the initial condition y(0) = 3, and the input is x(t) eu(t) as in 5(a). Can you find an initial condition for the derivative of the output, y'(0-), such that y(t) does not blow up as t gets large? If so, specify the value of the initial condition. If not, say why not. Zero input response 5(64(5) -4(0))-(0)-(sy (5) - 4(0))-2Y(=0 -ylo 5²-s-2) Y(St) = sy(o-) -y (σ`¯)+y' (0¯ ) Y(5) 2 35 - 3+ y' (0°) 35-3+4(0) (5-2) (5+1) A = B + 5-2 5+1 A = 6-3+y' (0-) = 1+5607/3 3 라 Need A = -1/3 to cancel out e²t term in zero state response | + 4 (0¯ ) = -1/2 =)) y ( 0 ) == 4 3
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