Practice 7. Properties Involving Unit Step (9.1.4) - Laplace Transform of Unit Step Function

Practice: 7. Properties Involving Unit Step

Lesson 9.1.4Laplace Transform of Unit Step Function

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9 questions

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6 sample questions

Question 1.
What is the definition of the unit step function?
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Think about how this function activates at a certain point.
Question 2.
Write down the formula for the Laplace Transform of a unit step function.
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Look at the standard results section in your notes.
3Question 3.
What is the main property of the unit step function?
- It is continuous everywhere
- It is zero before a certain time and one afterwards
- It oscillates between -1 and 1
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Think about its definition.
4Question 4.
True or False: The Laplace Transform preserves the linearity property.
- True
- False
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Consider how we can add transforms.
Question 5.
Given the function f(t) = 3(t-4)u(t-4), derive the Laplace Transform.
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Use integration by parts along with the second shifting theorem.
Question 6.
Design a model for a mechanical system where a unit step function is critical. Explain how you would apply Laplace Transforms in this model.
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What happens to the system when the force is suddenly applied?

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