Practice Properties Of Laplace Transforms (15.7) - Fourier Integral to Laplace Transforms

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6 sample questions

Question 1.
What does the linearity property of the Laplace transform state?
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Think about breaking down functions.
Question 2.
What is the formula for the First Shifting Theorem?
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Remember the shift around 's'!
3Question 3.
What is the formula for the linearity property of the Laplace transform?
- L{af(t)} + L{bg(t)}
- aL{f(t)} + bL{g(t)}
- a + b
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Focus on how you can distribute the transform.
4Question 4.
True or False: The First Shifting Theorem states that L{e^{it}f(t)} = F(s+i).
- True
- False
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Remember how the shift occurs.
Question 5.
Using the properties of Laplace transforms, solve the differential equation y'' + 3y' + 2y = Heaviside(t-2), where Heaviside is a unit step function.
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Use the properties to separate the functions effectively.
Question 6.
Demonstrate solving a second-order ODE using the First Shifting Theorem applied to the function e^{5t}sin(t).
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Identify how the shift impacts the s variable.

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