Question

3S4+10S3+5S2+S+2=0

Judge the stability of the system...

Answer #1

Determine the stability region using the Jury criterion for a
system whose characteristic equation P(z). Plot the stability
region on a plane determined by a-k.
P(z)=z^4+kz^3+2z^2+az+3=0

Solve and classify the type and stability of the origin for the
system
x'= -x
y'= -y
I am struggling to find the eigenvalues when the matrix ends up
being a 4x4 of 0

If the results of a steady-state stability analysis determine
that the system isn't stable what system actions might be taken
(for example, do you make changes to operating points, do you make
system configuration changes, etc)? How about if it was the result
of a transient stability analysis that predicted the system would
not be stable?

Judge Dullard is a trial judge in State X. He is in a quandary
over a recent case filed in his court. There are several state
Supreme Court cases from the 1960s and 1970s applying a common law
rule that is the opposite of a rule stated in a 1982 statute. He
believes the rule contained in the statute is bad public policy and
the common law rule is better. How should he decide this case?
Explain how the doctrine...

Sketch the phase portrait of y” - y’ - 6y = 0, y(0) = 2,
y’(0) = 3 as an autonomous system of two first order equations and
discuss the stability and the long time behavior of the
solutions.

Determine the stability region using the Schur-Cohn criterion
for a system whose characteristic equation P(z).
P(z)=z^3 +0.5z^2 +kz-k=0

Set up the linear system for the clamped cubic spline S that
interpolates the data f(0) = 1, f(2) = 9, f(3) = 28 and satisfies S
0 (0) = 0 and S 0 (3) = 27.

Special Relativity and electricity problem
Assume that in the reference system S, B = 0. In S
electrically charged particle moves with a particle with electric
charge q and speed w. Let S 'be a reference system that moves with
velocity v in the direction of the 1st axis seen from S.
Calculate the Lorentz force on the particle in the reference
system S 'by finding the electromagnetic field in S'. Then use the
transformation formulas for force to find the...

Solve each initial value problem, then classify the type
and stability of the critical point at (0,0) of each
system:
x1'=4x1+x2; x2'=-4x1+8x2
x1(0)=12; x2(0)=-6

Consider the linear first order system [16]
x′ = x + y (1) y′ =4x−2y. (2)
(a) Determine the equilibria of System (1)-(2) as well as their
stability. [6]
(b) Compute the general solution of System (1)-(2). [6]
(c) Determine the solution of the initial value problem
associated with System (1)-(2), with initial condition x(0) = 1,
y(0) = 2.

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