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b) Consider a system defined by the ordinary differential equation d²y(t) dt² dy(t) +6- - 27y(t) = 4- dt du(t) dt +12u(t) The initial conditions are defined as y(0¯) = 2 and y'(0) = 0. (i) Obtain the zero-input response of the system. Obtain the characteristic polynomial and the modes. (ii) Obtain the transfer function G(s) = Y(s)/U(s) of the system in an irreducible form. Discuss whether you can detect all the modes of the system directly from the zero-state response.

b) Consider a system defined by the ordinary differential equation d²y(t) dt² dy(t) +6- - 27y(t) = 4- dt du(t) dt +12u(t) The initial conditions are defined as y(0¯) = 2 and y'(0) = 0. (i) Obtain the zero-input response of the system. Obtain the characteristic polynomial and the modes. (ii) Obtain the transfer function G(s) = Y(s)/U(s) of the system in an irreducible form. Discuss whether you can detect all the modes of the system directly from the zero-state response.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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b) Consider a system defined by the ordinary differential equation d²y(t) dt² dy(t) +6- - 27y(t) = 4- dt du(t) dt +12u(t) The initial conditions are defined as y(0¯) = 2 and y'(0) = 0. (i) Obtain the zero-input response of the system. Obtain the characteristic polynomial and the modes. (ii) Obtain the transfer function G(s) = Y(s)/U(s) of the system in an irreducible form. Discuss whether you can detect all the modes of the system directly from the zero-state response.
Transcribed Image Text:b) Consider a system defined by the ordinary differential equation d²y(t) dt² dy(t) +6- - 27y(t) = 4- dt du(t) dt +12u(t) The initial conditions are defined as y(0¯) = 2 and y'(0) = 0. (i) Obtain the zero-input response of the system. Obtain the characteristic polynomial and the modes. (ii) Obtain the transfer function G(s) = Y(s)/U(s) of the system in an irreducible form. Discuss whether you can detect all the modes of the system directly from the zero-state response.
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