Practice Examples - 1.8 | 4. Second Shifting Theorem | Mathematics - iii (Differential Calculus) - Vol 1
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Examples

1.8 - Examples

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

Define the Heaviside step function.

💡 Hint: Consider how the function behaves over different time intervals.

Question 2 Easy

What does the Second Shifting Theorem state?

💡 Hint: Recall the notation and the meaning of each variable.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the equation for the Second Shifting Theorem?

ℒ{f(t-a)u_a(t)} = e^{-as}F(s)
ℒ{f(t+a)u_a(t)} = e^{as}F(s)
ℒ{f(t)u_a(t)} = F(s)

💡 Hint: Focus on the role of the negative exponent.

Question 2

True or False: The Heaviside function is zero for all time.

True
False

💡 Hint: Consider when it activates.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

What is the Laplace transform of (t-3)^3u_3(t)? Provide a detailed solution.

💡 Hint: Remember to find the initial Laplace transform of t^3.

Challenge 2 Hard

Consider a system where the response to an input signal starts after a delay of 5 seconds. How would you mathematically represent the output in terms of the Second Shifting Theorem?

💡 Hint: Think about how time delays linearly translate in the Laplace domain.

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