Practice Laplace Transforms & Applications - 7 | 7. Multiplication by tn (Power of t) | Mathematics - iii (Differential Calculus) - Vol 1
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Laplace Transforms & Applications

7 - Laplace Transforms & Applications

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is the basic definition of Laplace Transform?

💡 Hint: Think of the form L{f(t)}.

Question 2 Easy

If L{sin(at)} = a/(s^2 + a^2), what is L{t sin(at)}?

💡 Hint: Remember to differentiate!

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the formula for the multiplication by tn property in Laplace Transforms?

L{tn f(t)} = (-1)^n * d^n F(s)/ds^n
L{tn f(t)} = d^n L{f(t)}/ds^n
L{tn f(t)} = n! * L{f(t)}

💡 Hint: Remember the alternating sign factor!

Question 2

True or False: Multiplication by tn does not simplify any differential equation.

True
False

💡 Hint: Think about how we convert functions!

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Derive L{t^4e^(bt)} and explain how you can use the multiplication by tn property in this scenario.

💡 Hint: Start with the first derivative and track your steps!

Challenge 2 Hard

Consider a control system described by L{h(t)}. How would you illustrate time delays using the multiplication by tn property?

💡 Hint: Relate the concepts to real-world system behaviors!

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