Practice 7. Properties Involving Unit Step - 9.1.4 | 9. Laplace Transform of Unit Step Function | Mathematics - iii (Differential Calculus) - Vol 1
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9.1.4 - 7. Properties Involving Unit Step

Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What is the definition of the unit step function?

πŸ’‘ Hint: Think about how this function activates at a certain point.

Question 2

Easy

Write down the formula for the Laplace Transform of a unit step function.

πŸ’‘ Hint: Look at the standard results section in your notes.

Practice 4 more questions and get performance evaluation

Interactive Quizzes

Engage in quick quizzes to reinforce what you've learned and check your comprehension.

Question 1

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

πŸ’‘ Hint: Think about its definition.

Question 2

True or False: The Laplace Transform preserves the linearity property.

  • True
  • False

πŸ’‘ Hint: Consider how we can add transforms.

Solve 1 more question and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

Given the function f(t) = 3(t-4)u(t-4), derive the Laplace Transform.

πŸ’‘ Hint: Use integration by parts along with the second shifting theorem.

Question 2

Design a model for a mechanical system where a unit step function is critical. Explain how you would apply Laplace Transforms in this model.

πŸ’‘ Hint: What happens to the system when the force is suddenly applied?

Challenge and get performance evaluation