Practice Laplace Transforms & Applications (1) - Laplace Transform of Derivatives

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6 questions · about 4 min · pass mark 70%. Hints available.
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3 questions · about 2 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
What is the Laplace Transform of a constant function, L{1}?
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Consider how the Laplace Transform deals with constants.
Question 2.
Write down the formula for L{f′(t)}.
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Think about the first derivative in the Laplace domain.
3Question 3.
What is the formula for the Laplace Transform of the first derivative?
- L{f′(t)} = sF(s) - f(0)
- L{f′(t)} = sF(s) + f(0)
- L{f′(t)} = F(s) - sf(0)
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Focus on the relationship between derivatives and algebraic transformations.
4Question 4.
True or False: The Laplace Transform can only be applied to linear differential equations.
- True
- False
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Remember the nature of types of differential equations.
Question 5.
Using Laplace Transforms, derive the solution for the system y'' + 4y' + 4y = 0, y(0) = 1, y'(0) = 0.
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Apply the transformations step by step for clarity.
Question 6.
Demonstrate the use of Laplace Transforms in finding L{e^at sin(bt)}.
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Plug into the transformation formulas wisely.

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