Considered the following differential equation dªy dy dt2 dt +2y=0 (A) What are the time constants in the solutions to this homogeneous equation? (B) Say what we defined to be the settling time of a system. (C) What is the settling time of this system? Consider the following difference equation (k+2)-(+1)+(k)=0 (D) What are the roots of the characteristic polynomial? What are the two linearly independent solutions? (E) By how much does each solution decay each time step? (F) If the samples are taken at t = kT, and Tis 1/10, what is the time constant associated with each solution? What is the settling time associated with each solution? (G) How do the answers in part (F) change when T is 1/100?

Considered the following differential equation dªy dy dt2 dt +2y=0 (A) What are the time constants in the solutions to this homogeneous equation? (B) Say what we defined to be the settling time of a system. (C) What is the settling time of this system? Consider the following difference equation (k+2)-(+1)+(k)=0 (D) What are the roots of the characteristic polynomial? What are the two linearly independent solutions? (E) By how much does each solution decay each time step? (F) If the samples are taken at t = kT, and Tis 1/10, what is the time constant associated with each solution? What is the settling time associated with each solution? (G) How do the answers in part (F) change when T is 1/100?

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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