Practice Laplace Transforms & Applications (1)

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9 questions

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6 sample questions

Question 1.
What is the Heaviside Step Function?
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Think about when a system is turned on.
Question 2.
State the Second Shifting Theorem in your own words.
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How does the theorem modify the transform?
3Question 3.
What does the Second Shifting Theorem allow us to do?
- Transform delayed functions
- Only transform continuous functions
- Forget about delays
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Focus on the purpose of the theorem.
4Question 4.
True or False: The Heaviside step function is always one.
- True
- False
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Remember its piecewise nature.
Question 5.
Using the Second Shifting Theorem, find the Laplace transform for f(t - 3)u(t) if f(t) = e^{2t}.
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How does your shift affect the exponential?
Question 6.
A mechanical system has a torque response represented by f(t) = sin(t) which initiates after 5 seconds. Calculate its Laplace transform.
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Modify the sine function using the theorem.

5 more questions in this section. Enroll free to practise them all.