Consider a system defined by the ordinary differential equation (ODE) dy(t) c) dy(t) du(t) -2- -48y(t) = (1+ 0. X) + (2 +0. Y)u(t) dt2 dt dt where X and Y are the last two digits of your student number. The input signal is a unit step function. The initial conditions are defined as y(0") = 1 and y(0-) = 2. For example, if your student number is c1700123, then the ODE is d'y(t) dy(t) 2 dt du(t) 48y(t) = 1.2 + 2.Зи (() dt %3D dt? Obtain the zero-input response of the system Obtain the characteristic polynomial
Consider a system defined by the ordinary differential equation (ODE) dy(t) c) dy(t) du(t) -2- -48y(t) = (1+ 0. X) + (2 +0. Y)u(t) dt2 dt dt where X and Y are the last two digits of your student number. The input signal is a unit step function. The initial conditions are defined as y(0") = 1 and y(0-) = 2. For example, if your student number is c1700123, then the ODE is d'y(t) dy(t) 2 dt du(t) 48y(t) = 1.2 + 2.Зи (() dt %3D dt? Obtain the zero-input response of the system Obtain the characteristic polynomial
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
X=2
Y=8
![c)
Consider a system defined by the ordinary differentlal equation (ODE)
dy(t)
dy(t)
- 48y(t) (1 +0.X)
du(t)
+ (2 +0. Y)u(t)
dt
dt
dt
where X and Y are the last two digits of your student number. The input signal
is a unit step function. The initial conditions are defined as y(0)=1 and
Y(0) = 2.
For example, if your student number is c1700123, then the ODEls
d'y(t)
dy(t)
2
dt
du(t)
48y(t) = 1.2
+ 2.3u(t)
dt
dt2
Obtain the zero-input response of the system Obtain the characteristic
polynomial.
Obtain the transfer function G(s) = Y(s)/U(s) of the system and classify
all poles and zeros. Is G(s) stable?
Compare the denominator of G(6) with the characteristic polynomial
Discuss the implications of their similarities and/or differences.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F492be3c1-b914-41aa-bea1-f6b572444887%2F79bea8ba-636e-4afd-8cbb-18724af7153c%2F2uwzaxe_processed.jpeg&w=3840&q=75)
Transcribed Image Text:c)
Consider a system defined by the ordinary differentlal equation (ODE)
dy(t)
dy(t)
- 48y(t) (1 +0.X)
du(t)
+ (2 +0. Y)u(t)
dt
dt
dt
where X and Y are the last two digits of your student number. The input signal
is a unit step function. The initial conditions are defined as y(0)=1 and
Y(0) = 2.
For example, if your student number is c1700123, then the ODEls
d'y(t)
dy(t)
2
dt
du(t)
48y(t) = 1.2
+ 2.3u(t)
dt
dt2
Obtain the zero-input response of the system Obtain the characteristic
polynomial.
Obtain the transfer function G(s) = Y(s)/U(s) of the system and classify
all poles and zeros. Is G(s) stable?
Compare the denominator of G(6) with the characteristic polynomial
Discuss the implications of their similarities and/or differences.
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