Practice Standard Result - 9.1.2 | 9. Laplace Transform of Unit Step Function | Mathematics - iii (Differential Calculus) - Vol 1
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Standard Result

9.1.2 - Standard Result

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is the value of u(t-5) when t = 3?

💡 Hint: Think about the definition of the unit step function.

Question 2 Easy

Write the expression for the Laplace Transform of u(t-4).

💡 Hint: Consider the standard result we've just discussed.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What does the unit step function u(t-a) equal for t < a?

0
1
Undefined

💡 Hint: Recall the definition of the unit step function.

Question 2

The Laplace Transform of u(t-a) is which of the following?

\\( \\frac{e^{-as}}{s} \\)
\\( \\frac{a}{s} \\)
s

💡 Hint: Consider the formula discussed in class.

2 more questions available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Derive the Laplace Transform of the function f(t) = (3t + 2)u(t-1). What is the transformed function?

💡 Hint: Break it down, and remember to apply the theorem after recognizing the step function.

Challenge 2 Hard

Model a mechanical system experiencing a sudden force at t = 5 seconds. Write the governing differential equation and solve using Laplace Transform.

💡 Hint: Apply the Laplace Transform for each term, recalling initial conditions.

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