Test: Laplace Transform- 1


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10 Questions MCQ Test Signals and Systems | Test: Laplace Transform- 1

Test: Laplace Transform- 1 for Electronics and Communication Engineering (ECE) 2023 is part of Signals and Systems preparation. The Test: Laplace Transform- 1 questions and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus.The Test: Laplace Transform- 1 MCQs are made for Electronics and Communication Engineering (ECE) 2023 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Laplace Transform- 1 below.
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Test: Laplace Transform- 1 - Question 1

Determine the Laplace transform of given signal.
Q. x(t) = u( t - 2)

Detailed Solution for Test: Laplace Transform- 1 - Question 1

Test: Laplace Transform- 1 - Question 2

Laplace transform of t2 sin⁡(2t).

Detailed Solution for Test: Laplace Transform- 1 - Question 2

We know that,

Here, f(t) = sin⁡(2t) => F(s) =
Hence,  L(t2sin(2t)) =

Test: Laplace Transform- 1 - Question 3

Determine the Laplace transform of given signal.
Q. x(t) = e-2tu(t+1)

Detailed Solution for Test: Laplace Transform- 1 - Question 3

Laplace transform e-at u(t) = 1/s+a

for all Re(s) > - Re(a)

e-2t u(t+1) = 1/(s+2)

Test: Laplace Transform- 1 - Question 4

Determine the Laplace transform of given signal.
Q. x(t) = e2tu(-t+2)

Detailed Solution for Test: Laplace Transform- 1 - Question 4


Test: Laplace Transform- 1 - Question 5

Determine the Laplace transform of given signal.
Q. x(t) = sin 5 t

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Test: Laplace Transform- 1 - Question 6

Determine the Laplace transform of given signal.
Q. x( t) = u(t) - u(t - 2)

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Test: Laplace Transform- 1 - Question 7

Determine the Laplace transform of given signal.
Q. x( t) = d/dt {te-1u(t)}

Detailed Solution for Test: Laplace Transform- 1 - Question 7


Test: Laplace Transform- 1 - Question 8

Determine the Laplace transform of given signal.
Q. x( t) = tu(t)*cos2πt u(t)

Detailed Solution for Test: Laplace Transform- 1 - Question 8


Test: Laplace Transform- 1 - Question 9

Determine the Laplace transform of given signal.
Q. x( t) = t3u(t)

Detailed Solution for Test: Laplace Transform- 1 - Question 9


Test: Laplace Transform- 1 - Question 10

Determine the Laplace transform of given signal.
Q. x(t) = u( t - 1) * e-2tu( t - 1)

Detailed Solution for Test: Laplace Transform- 1 - Question 10

L{−e-at u(t)} 

= ∫(∞ to −∞) −e-at u(t)e-stdt 

L{−e-at u(t)}

= ∫(∞ to 0) − e-(s+a)t dt

= - |e-(s+a)t/−(s+a)|∞ to 0

= −1/s+a

=> L{−e-2t u(t)} = -1/s+2

=> L{−e-2t u(t-1)} = e-(s+2)/s2 …………(1)

q(t) = L{u(t-1)}

= e-s/(s2)................(2)

Multiply (1) and (2)

= e-2(s+1)/(s+2)

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