Practice Laplace Transform: Basic Definition (7.3) - Multiplication by tn (Power of t)

Practice: Laplace Transform: Basic Definition

Lesson 7.3Multiplication by tn (Power of t)

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8 questions

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

Question 1.
What is the formula for the Laplace Transform?
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Look for the integral definition of the Laplace Transform.
Question 2.
What does differentiating a function mean?
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Think about how slopes of curves are determined.
3Question 3.
What is the general formula for the Laplace Transform?
- L{f(t)} = ∫[0,∞] e^(-st) f(t) dt
- L{f(t)} = ∫[0,∞] e^(st) f(t) dt
- L{f(t)} = ∫[0,∞] f(t)e^(st) dt
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Think about the integral form involving an exponential decay.
4Question 4.
True or False: The Multiplication by tn Property results in differentiation in the s-domain.
- True
- False
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Recall how differentiation affects functions in calculus.
Question 5.
Prove the multiplication by t^n property for n=2 by calculation, starting from L{f(t)}.
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Pay attention to the orders of differentiation and exponential decay in your integral expressions.
Question 6.
Using the properties of Laplace Transforms, solve for L{e^{2t}sin(3t)}. Express in terms of s.
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Identify the base transformation of e^{2t} and use it effectively!

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