Q5) An LTI system is characterized by thedifferential equation below:d²d= y(t)+ = y(t)+16.25y(t) == x(1)dt²dtdta) Write the characteristic equation.b) Find the characteristic roots.c) Write the form of the zero-input response.d) Write the final zero-input response if yzı(0)=0 anddyzi(0)/dt=2.e) Plot the final zero-input response inMatlab/Octave and select the correct graph on theside:f) What are the characteristic modes for this system?00.50-0.5005(1)5(3)10100.5-0.50.10-0.1-0.2Am005(2)5(4)1010

Answered: Q5) An LTI system is characterized by…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

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Q5) An LTI system is characterized by the
differential equation below:
d²
d
= y(t)+ = y(t)+16.25y(t) == x(1)
dt²
dt
dt
a) Write the characteristic equation.
b) Find the characteristic roots.
c) Write the form of the zero-input response.
d) Write the final zero-input response if yzı(0)=0 and
dyzi(0)/dt=2.
e) Plot the final zero-input response in
Matlab/Octave and select the correct graph on the
side:
f) What are the characteristic modes for this system?
0
0.5
0
-0.5
0
0
5
(1)
5
(3)
10
10
0.5
-0.5
0.1
0
-0.1
-0.2
Am
0
0
5
(2)
5
(4)
10
10

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Given:

Differential equation of a LTI system

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a) characteristic equation

b) the characteristic roots

c) the form of Zero input response

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