Solve for x(t) in the following differential equation using Laplace transforms: [x(?}]+ 7[x(;}]+ 12x(t)=0 d with initial conditions x(0 }=2 and (x(t}),-. = -4 dt
Solve for x(t) in the following differential equation using Laplace transforms: [x(?}]+ 7[x(;}]+ 12x(t)=0 d with initial conditions x(0 }=2 and (x(t}),-. = -4 dt
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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![Al-Iraqia university
College of engineering
Network Dept.
Signals and Systems
Q1)
Solve for x(t) in the following differential equation using
Laplace transforms:
d
z[x(t)]+7[x(t}]+12x(t)=0
dt?
dt
with initial conditions x(0 }= 2 and
=-4
t=0
Q2)
Solve the following difference equation by use of the
z transform method:
x(k + 2) + 3x(k + 1) + 2x(k) = 0,
x(0) %3D 0, х(1) %3D1
Q3)
Given the sequence x(n)={0, 1, 2, 3}
a) Calculate the DFT X(k).
b) Calculate the inverse DFT x(n) from X(k) obtained in (a).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5d2ad462-8281-4391-b31e-1d124e17c96f%2Fa2171698-35e0-4ec7-a147-9a4120739ed2%2F3v0pmbe_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Al-Iraqia university
College of engineering
Network Dept.
Signals and Systems
Q1)
Solve for x(t) in the following differential equation using
Laplace transforms:
d
z[x(t)]+7[x(t}]+12x(t)=0
dt?
dt
with initial conditions x(0 }= 2 and
=-4
t=0
Q2)
Solve the following difference equation by use of the
z transform method:
x(k + 2) + 3x(k + 1) + 2x(k) = 0,
x(0) %3D 0, х(1) %3D1
Q3)
Given the sequence x(n)={0, 1, 2, 3}
a) Calculate the DFT X(k).
b) Calculate the inverse DFT x(n) from X(k) obtained in (a).
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