Q1- Determine the Laplace transform and ROC of the following signals: I. x(t) = e5tu(-t + 3) († - 1)n = (1)x П. III. x(t) = e-2tu(t) +e-3tu(t)
Q1- Determine the Laplace transform and ROC of the following signals: I. x(t) = e5tu(-t + 3) († - 1)n = (1)x П. III. x(t) = e-2tu(t) +e-3tu(t)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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![Q1- Determine the Laplace transform and ROC of the following signals:
I.
x(t) = u(t - 4)
II.
x(t) = e5tu(-t + 3)
III.
x(t) = e-2tu(t) + e-3tu(t)
IV. x(t) = e-t(t – 3)u(t – 3)
Q2-
Find the inverse Laplace transform of
3s+4
a) X(s) =
(s+1)(s+2)²
2
%3D
s-2
Q3-
The relationship between the input x(t) and output y(t) of a causal system is described by the
differential equation given below. Use Laplace transforms to determine the transfer function and
impulse response of the system.
d
d?
d
drz y(t) + 3y(t) + 2y(t) = 3x(t) +x(t)
dt°
dt
Q4-
If we have
3s +1
-31
H(s) =
x(t) = e*u(t)
s² +6s + 5'
Find y(t)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0a6d97dd-0b81-42da-9feb-7be1a235ed32%2F3c06b78b-f588-4302-a967-0a2a42ada199%2Fwnu2n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Q1- Determine the Laplace transform and ROC of the following signals:
I.
x(t) = u(t - 4)
II.
x(t) = e5tu(-t + 3)
III.
x(t) = e-2tu(t) + e-3tu(t)
IV. x(t) = e-t(t – 3)u(t – 3)
Q2-
Find the inverse Laplace transform of
3s+4
a) X(s) =
(s+1)(s+2)²
2
%3D
s-2
Q3-
The relationship between the input x(t) and output y(t) of a causal system is described by the
differential equation given below. Use Laplace transforms to determine the transfer function and
impulse response of the system.
d
d?
d
drz y(t) + 3y(t) + 2y(t) = 3x(t) +x(t)
dt°
dt
Q4-
If we have
3s +1
-31
H(s) =
x(t) = e*u(t)
s² +6s + 5'
Find y(t)
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