Practice Application Scenarios - 1.7 | 3. Topic 3: First Shifting Theorem | Mathematics - iii (Differential Calculus) - Vol 1
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Application Scenarios

1.7 - Application Scenarios

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

Find the Laplace Transform of e^3t * cos(5t).

💡 Hint: Start with the transform of cos(bt).

Question 2 Easy

What shift do we apply for e^{-2t} f(t)?

💡 Hint: Remember the sign when applying the shift.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the result of applying the First Shifting Theorem to e^{2t} * sin(3t)?

s^2 + 9
(s-2)^2 + 9
(s+2)^2 + 9

💡 Hint: Remember the shift rule defined by the theorem.

Question 2

True or False: The conditions s > Re(a) must be met when applying the First Shifting Theorem.

True
False

💡 Hint: Think about the nature of the exponentials involved.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Using the First Shifting Theorem, compute the Laplace Transform of e^{-2t}cos(6t).

💡 Hint: What is the standard Laplace Transform for cos(bt)?

Challenge 2 Hard

Explain how the presence of e^{4t} affects the stability of the system modeled by the equation.

💡 Hint: Consider the implications of shifting the transform.

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