Laplace Transform Quiz: Test!

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| By Dasari Nagaraju

Dasari Nagaraju

Community Contributor

Quizzes Created: 1 | Total Attempts: 1,118

Questions: 10 | Attempts: 1,122 | Updated: Mar 21, 2023

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Questions and Answers

1.
- A.
  
  True
- B.
  
  False
Correct Answer
A. True
2.
- A.
  
  True
- B.
  
  False
Correct Answer
A. True
3.
- A.
  
  True
- B.
  
  False
Correct Answer
B. False
4.
- A.
  
  True
- B.
  
  False
Correct Answer
B. False
5.

L(f * g) = L(f).L(g)
- A.
  
  True
- B.
  
  False
Correct Answer
A. True

Explanation
The given statement is the multiplication property of the Laplace transform. According to this property, the Laplace transform of the product of two functions is equal to the product of their individual Laplace transforms. Therefore, the statement is true.

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1
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6.

L^-1(F(s) + G(s)) = f(t)+ g(t)
- A.
  
  True
- B.
  
  False
Correct Answer
A. True

Explanation
The given equation represents the Laplace transform of the sum of two functions, F(s) and G(s), which is equal to the sum of the time-domain representations of those functions, f(t) and g(t). This is a fundamental property of the Laplace transform, known as the linearity property. Therefore, the statement is true.

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7.

L^-1(F(s) G(s)) = f(t) g(t)
- A.
  
  True
- B.
  
  False
Correct Answer
B. False

Explanation
The given equation L-1(F(s) G(s)) = f(t) g(t) is false. The Laplace inverse of the product of two Laplace transforms is not equal to the product of their inverse transforms. Therefore, the statement is incorrect.

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8.
- A.
  
  True
- B.
  
  False
Correct Answer
A. True
9.

L(f ‘) = sL(f) – f(0)
- A.
  
  True
- B.
  
  False
Correct Answer
A. True

Explanation
The given equation L(f') = sL(f) - f(0) is a valid equation in Laplace transform theory. It states that the Laplace transform of the derivative of a function f is equal to s times the Laplace transform of f minus the value of f at 0. This equation holds true and is commonly used in solving differential equations using Laplace transforms.

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10.

L(f(t)/t) = -F’(s)
- A.
  
  True
- B.
  
  False
Correct Answer
B. False

Explanation
The given equation L(f(t)/t) = -F'(s) is not true. This is because the left-hand side of the equation represents the Laplace transform of the function f(t)/t, while the right-hand side represents the derivative of the Laplace transform of the function F(s). These two expressions are not equivalent, so the equation is false.

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0

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Current Version
Mar 21, 2023

Quiz Edited by
ProProfs Editorial Team
Mar 16, 2018

Quiz Created by
Dasari Nagaraju

Laplace Transform Quiz: Test!

L(f * g) = L(f).L(g)

L-1(F(s) + G(s)) = f(t)+ g(t)

L-1(F(s) G(s)) = f(t) g(t)

L(f ‘) = sL(f) – f(0)

L(f(t)/t) = -F’(s)

L^-1(F(s) + G(s)) = f(t)+ g(t)

L^-1(F(s) G(s)) = f(t) g(t)