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1. Consider the following LTI system. d²y dy du +7 +6y= -- +2u, t≥0 dt² dt dt a) What is the impulse response of the system? Recall, h(t) = L-¹(H(s)). b) What are poles and zeros of the system? c) Suppose the initial condition of the system is y(0) = 1 and y'(0) = 4. What is the zero-input response of the system? d) Consider an input u(t) = (1 + et) 1(t) to the system. What is the zero-state response of the system for this input? e) Suppose, the initial condition was y(0) = -2 and y'(0) = -8 and the input is u(t)=(1+e) 1(t). What will be the total response of the system? You should be able to answer this using the linearity property of the system and your answers in part b and part c without taking any inverse Laplace transform.

1. Consider the following LTI system. d²y dy du +7 +6y= -- +2u, t≥0 dt² dt dt a) What is the impulse response of the system? Recall, h(t) = L-¹(H(s)). b) What are poles and zeros of the system? c) Suppose the initial condition of the system is y(0) = 1 and y'(0) = 4. What is the zero-input response of the system? d) Consider an input u(t) = (1 + et) 1(t) to the system. What is the zero-state response of the system for this input? e) Suppose, the initial condition was y(0) = -2 and y'(0) = -8 and the input is u(t)=(1+e) 1(t). What will be the total response of the system? You should be able to answer this using the linearity property of the system and your answers in part b and part c without taking any inverse Laplace transform.

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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1. Consider the following LTI system. d²y dy du +7 +6y= -- +2u, t≥0 dt² dt dt a) What is the impulse response of the system? Recall, h(t) = L-¹(H(s)). b) What are poles and zeros of the system? c) Suppose the initial condition of the system is y(0) = 1 and y'(0) = 4. What is the zero-input response of the system? d) Consider an input u(t) = (1 + et) 1(t) to the system. What is the zero-state response of the system for this input? e) Suppose, the initial condition was y(0) = -2 and y'(0) = -8 and the input is u(t)=(1+e) 1(t). What will be the total response of the system? You should be able to answer this using the linearity property of the system and your answers in part b and part c without taking any inverse Laplace transform.
Transcribed Image Text:1. Consider the following LTI system. d²y dy du +7 +6y= -- +2u, t≥0 dt² dt dt a) What is the impulse response of the system? Recall, h(t) = L-¹(H(s)). b) What are poles and zeros of the system? c) Suppose the initial condition of the system is y(0) = 1 and y'(0) = 4. What is the zero-input response of the system? d) Consider an input u(t) = (1 + et) 1(t) to the system. What is the zero-state response of the system for this input? e) Suppose, the initial condition was y(0) = -2 and y'(0) = -8 and the input is u(t)=(1+e) 1(t). What will be the total response of the system? You should be able to answer this using the linearity property of the system and your answers in part b and part c without taking any inverse Laplace transform.
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