1- Find the Laplace transform and the corresponding ROC of the following signals. a) x(t) = [e-2t + et cos(3t)]u(t) b)x(t) = e-altl = e-atu(t) + eatu(-t), consider a>0. c) x(t) = 8(t) + 8(t – 1) + 8(t - 2) %3D %3D ハ 1) u(1)
1- Find the Laplace transform and the corresponding ROC of the following signals. a) x(t) = [e-2t + et cos(3t)]u(t) b)x(t) = e-altl = e-atu(t) + eatu(-t), consider a>0. c) x(t) = 8(t) + 8(t – 1) + 8(t - 2) %3D %3D ハ 1) u(1)
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
![Tutorial Laplace Transform
1- Find the Laplace transform and the corresponding ROC of the following
signals.
a) x(t) = [e-2 + e' cos(3t)]u(t)
b)x(t) = e-altl = e-atu(t) + eatu(-t) , consider a>0.
c) x(t) = 8(t) + 8(t – 1) + 8(t – 2)
d) x() %3D и(-1) - и(1)
e) x(t) = e-3t Lo T sin(2t) u(t)dt
f) x(t) = [r³ +sin(2t)]u(t)dr
g) x(t) = t2e-2t cos(5t) u(t - 1)
2- Find the inverse of Laplace transform
s-1
, Re[s]>-3
a)
s2(s+3)
s+5
, i) Re[s]> 3 ii) Re[s]>-1 ii) Re[s]<3 iii) -1<Re[s]< 3
b)
(s+1)(s-3)
s+5
c)
(s-1)(s+1)2
Re[s]> 1
s+5
d)
(s-1)(s-2)(s-3)'
i) Re[s]> 3 ii) Re[s]<1
iii) 1<Re[s]< 2.
3-Consider the LTI system with the input x(t) = e-tu(t) and the impulse
response h(t) = e-2tu(t).
a) Determine the Laplace transform of x(t) and h(t).
b) Using convolutional property, determine the Laplace transform of the output
y(t). Find the ROC for each case.
4- Consider the signal y(t) = x1(t - 2) * x2(-t + 3) where x1 (t) = e 2u(t)
and x2(t) = e3tu(t). Determine the Laplace transform of y(t) using the
properties. Also find the ROC.
s+1
5- The transfer function of causal LTI system is H(s) =
(s+1)(s+3)
Determine the response y(t) when the input x(t) = e-lti, for the following region
of convergence :) Re[s]> -3 ii) Re[s]<-1
iii) -1>Re[s]> -3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F42cad03e-e8bb-4731-a6ed-ff061b1406e8%2Fcb36130f-1823-49cc-b3de-0eb89b3ef011%2Framgnqd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Tutorial Laplace Transform
1- Find the Laplace transform and the corresponding ROC of the following
signals.
a) x(t) = [e-2 + e' cos(3t)]u(t)
b)x(t) = e-altl = e-atu(t) + eatu(-t) , consider a>0.
c) x(t) = 8(t) + 8(t – 1) + 8(t – 2)
d) x() %3D и(-1) - и(1)
e) x(t) = e-3t Lo T sin(2t) u(t)dt
f) x(t) = [r³ +sin(2t)]u(t)dr
g) x(t) = t2e-2t cos(5t) u(t - 1)
2- Find the inverse of Laplace transform
s-1
, Re[s]>-3
a)
s2(s+3)
s+5
, i) Re[s]> 3 ii) Re[s]>-1 ii) Re[s]<3 iii) -1<Re[s]< 3
b)
(s+1)(s-3)
s+5
c)
(s-1)(s+1)2
Re[s]> 1
s+5
d)
(s-1)(s-2)(s-3)'
i) Re[s]> 3 ii) Re[s]<1
iii) 1<Re[s]< 2.
3-Consider the LTI system with the input x(t) = e-tu(t) and the impulse
response h(t) = e-2tu(t).
a) Determine the Laplace transform of x(t) and h(t).
b) Using convolutional property, determine the Laplace transform of the output
y(t). Find the ROC for each case.
4- Consider the signal y(t) = x1(t - 2) * x2(-t + 3) where x1 (t) = e 2u(t)
and x2(t) = e3tu(t). Determine the Laplace transform of y(t) using the
properties. Also find the ROC.
s+1
5- The transfer function of causal LTI system is H(s) =
(s+1)(s+3)
Determine the response y(t) when the input x(t) = e-lti, for the following region
of convergence :) Re[s]> -3 ii) Re[s]<-1
iii) -1>Re[s]> -3
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
