1) Consider the ALDS -9 -91 x=1 0 0 x. 0 1 0 a) Draw a block diagram for this system. b) Find the general form of x(t) given the initial condition x(0)? c) Find the eigenvalues of A. d) Find the right eigenvectors of A. e) Find the left eigenvectors of A. f) Let x(0) (0-1 1). Plot x(t) for t≤ 5. == == g) Let x(0) = (010). Plot x(t) for t≤5. Discuss the qualitative behavior of x(t) for this x(0)? h) Let x(0) = (1-1 1). Plot x(t) for t≤ 5. Discuss the qualitative behavior of x(t) for this x(0)? i) Let w = (0.11 0 1) and x(0) = (0-1 1). Plot w³ x(t) for t≤ 5. What can you say about the qualitative behavior of w² x(t)?
1) Consider the ALDS -9 -91 x=1 0 0 x. 0 1 0 a) Draw a block diagram for this system. b) Find the general form of x(t) given the initial condition x(0)? c) Find the eigenvalues of A. d) Find the right eigenvectors of A. e) Find the left eigenvectors of A. f) Let x(0) (0-1 1). Plot x(t) for t≤ 5. == == g) Let x(0) = (010). Plot x(t) for t≤5. Discuss the qualitative behavior of x(t) for this x(0)? h) Let x(0) = (1-1 1). Plot x(t) for t≤ 5. Discuss the qualitative behavior of x(t) for this x(0)? i) Let w = (0.11 0 1) and x(0) = (0-1 1). Plot w³ x(t) for t≤ 5. What can you say about the qualitative behavior of w² x(t)?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:1) Consider the ALDS
-9 -91
x=1
0 0 x.
0
1
0
a) Draw a block diagram for this system.
b) Find the general form of x(t) given the initial condition x(0)?
c) Find the eigenvalues of A.
d) Find the right eigenvectors of A.
e) Find the left eigenvectors of A.
f) Let x(0) (0-1 1). Plot x(t) for t≤ 5.
==
==
g) Let x(0) = (010). Plot x(t) for t≤5. Discuss the qualitative behavior of x(t) for this
x(0)?
h) Let x(0) = (1-1 1). Plot x(t) for t≤ 5. Discuss the qualitative behavior of x(t) for this
x(0)?
i) Let w = (0.11 0 1) and x(0) = (0-1 1). Plot w³ x(t) for t≤ 5. What can you say
about the qualitative behavior of w² x(t)?
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