An LTI system is defined by the equationd?y(t)+ 4 dy(t) + 4y(t) = dx(t) + 0.5x(t)dtdt(a) Find the characteristic equation, characteristic roots and characteristic modes of thissystem(b) Comment on the stability of the system.(c) Find y.(t), the zero-input component of the response fort 2 0, if the initial conditionsare y. (0-) = 3 and yo(0 –) = -4(d) Mathematically derive an expression for h(t), the impulse response of the system.(e) Using the convolution tables and the result of part (d), find the zero-state output for thesystem given the input x(t) = e-stu(t)(f) What is the total system response based on the conditions and input specified above?(g) What is the natural response and what is the forced response of this system?(h) Using Matlab, plot the impulse and step responses and frequency response (magnitudeand phase) of this system directly from the differential equation.Hint: Sample code given in Module 6 may be used, but frequency range will have tobe increased.(1) Compare the impulse response plot from part (h) to the expression from part (d).Comment on the overall shape and specific points on the plot that confirm that they areequivalent.G) Using the frequency response plots from part (h), determine the output of the systemif x(t) = 8+ 10 cos(t – 20°) + 6 cos(30t + 30°)Hint: You can use the data cursorfeature to read the coordinate values off theplots.

An LTI system is defined by the equation d*y(t) +4 ¢y() + 4y(t) = dx(e) + 0.5x(t) dt dt dt (a) Find the characteristic equation, characteristic roots and characteristic modes of this system (b) Comment on the stability of the system. (c) Find y.(t), the zero-input component of the response fort 2 0, if the initial conditions are y. (0-) = 3 and y,(0 -) = -4

An LTI system is defined by the equation d*y(t) +4 ¢y() + 4y(t) = dx(e) + 0.5x(t) dt dt dt (a) Find the characteristic equation, characteristic roots and characteristic modes of this system (b) Comment on the stability of the system. (c) Find y.(t), the zero-input component of the response fort 2 0, if the initial conditions are y. (0-) = 3 and y,(0 -) = -4

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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