Practice Transform of Shifted Functions - 15.12.2 | 15. Fourier Integral to Laplace Transforms | Mathematics (Civil Engineering -1)
K12 Students

Academics

AI-Powered learning for Grades 8–12, aligned with major Indian and international curricula.

Professionals

Professional Courses

Industry-relevant training in Business, Technology, and Design to help professionals and graduates upskill for real-world careers.

Games

Interactive Games

Fun, engaging games to boost memory, math fluency, typing speed, and English skills—perfect for learners of all ages.

Typing
Memory
Math
English Adventures
Knowledge

15.12.2 - Transform of Shifted Functions

Enroll to start learning

You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.

Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

Define a shifted function in your own words.

💡 Hint: Think about when you add something to a system.

Question 2

Easy

What is the purpose of the unit step function in shifted functions?

💡 Hint: Consider how the function behaves before and after the delay.

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 formula for the Laplace transform of a shifted function?

  • L{f(t-a)u(t-a)} = e^{-as}F(s)
  • L{f(t+a)u(t+a)} = e^{as}F(s)
  • L{f(t-u(t-a))} = F(s)

💡 Hint: Focus on how the shift modifies the standard Laplace transformation.

Question 2

True or False: The unit step function allows a function to begin analysis at t<0.

  • True
  • False

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

Solve and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

A system experiences a load that starts fluctuating after 4 seconds. If the function describing load fluctuation is f(t) = sin(t), express its Laplace transform and explain the significance of transformations in engineering.

💡 Hint: Reflect on how you account for the shift when applying the transform.

Question 2

Model a scenario where material is added to a structure 5 seconds after construction begins. Define the function and calculate its Laplace transform.

💡 Hint: Break down the process into defining the load before transforming.

Challenge and get performance evaluation