Practice Linearity (9.1.5.1) - Laplace Transform of Unit Step Function

Practice: Linearity

Lesson 9.1.5.1Laplace Transform of Unit Step Function

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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 it models sudden changes.
Question 2.
What is the Laplace Transform of $u(t)$ ?
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Remember it's the transform of the basic unit step function.
3Question 3.
What is the Laplace Transform of $u(t-a)$ ?
- \$ \\frac{1}{s} \$
- \$ \\frac{e^{-as}}{s} \$
- \$ s \$
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Focus on how the step function impacts transformation.
4Question 4.
True or False: The unit step function is always equal to 1.
- True
- False
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Recall the conditions for the unit step function.
Question 5.
Consider a mechanical system where a force is applied at t=2 seconds. Model the system using the unit step function and derive the Laplace Transform of the applied force.
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Think about the timing and impact of the function before and after the shift.
Question 6.
For the piecewise function defined as $f(t) = t \cdot u(t-1) + 2 \cdot u(t-2)$ , calculate its Laplace Transform.
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Separate each part according to the shifting theorem.

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