15.7.2 - First Shifting Theorem
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Practice Questions
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What is the First Shifting Theorem?
💡 Hint: Think about how the Laplace transform changes with exponential functions.
If f(t) = cos(t), how would you express L{e^{5t}cos(t)}?
💡 Hint: Remember to identify the original function before applying the theorem.
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Interactive Quizzes
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What does the First Shifting Theorem state?
💡 Hint: Focus on the relationship between exponential and Laplace transforms.
True or False: The First Shifting Theorem is used solely in theoretical mathematics.
💡 Hint: Think about where Laplace transforms are applied.
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Challenge Problems
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Apply the First Shifting Theorem to the function f(t) = e^{4t} * t^3 and find its Laplace transform.
💡 Hint: Calculate the basic Laplace transform first.
Explain how the First Shifting Theorem applies when analyzing a damped harmonic oscillator with an exponential decay factor added.
💡 Hint: Consider how damping impacts frequency responses.
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