Practice Multiplication By 't' In Time Domain Property (5.3.10) - Laplace Transform Analysis of Continuous-Time Systems
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Multiplication by 't' in Time Domain Property

Practice - Multiplication by 't' in Time Domain Property

Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

Find the transform of t * u(t).

💡 Hint: Use the property L{t * x(t)} = -d/ds [X(s)].

Question 2 Easy

What is the Laplace Transform of t * e^(at) u(t)?

💡 Hint: Find the transform of e^(at) first.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

Multiplying a signal by 't' results in which operation in the s-domain?

Addition
Differentiation
Multiplication

💡 Hint: Remember the property we discussed.

Question 2

True or False: The Laplace Transform of t * x(t) is equal to d/ds [X(s)].

True
False

💡 Hint: Check the negative sign in the property.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Given x(t) = t * e^(-2t) * u(t), find L{x(t)} using the multiplication by 't' property.

💡 Hint: Don't forget to differentiate with care!

Challenge 2 Hard

For x(t) = t^2 * sin(3t) u(t), compute its Laplace Transform.

💡 Hint: Remember to use the property iteratively for higher powers of t.

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Reference links

Supplementary resources to enhance your learning experience.