Practice Time-Shift for General Function - 9.1.5.2 | 9. Laplace Transform of Unit Step Function | Mathematics - iii (Differential Calculus) - Vol 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

9.1.5.2 - Time-Shift for General Function

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

What defines the unit step function?

💡 Hint: Think about what happens at the jump point.

Question 2

Easy

Write the Laplace Transform of u(t-a).

💡 Hint: Look for the exponential function in the formula.

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 unit step function?

  • A function that oscillates.
  • A function that stays constant.
  • A function that jumps at a specific point.

💡 Hint: Focus on the defining feature of the function.

Question 2

True or False: The Laplace Transform is used to convert functions from the frequency domain to time domain.

  • True
  • False

💡 Hint: Remember the direction of the transform.

Solve and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

A control system has an input that is turned on at t=3 seconds and remains on indefinitely. Describe how you would model this using the unit step function and derive the Laplace Transform.

💡 Hint: Start by writing down what happens at the time 3 seconds.

Question 2

You are given a mechanical system that each force is applied suddenly at intervals of 2 seconds. Explain how you would set up the differential equation using the Laplace Transform and the unit step function.

💡 Hint: How does the forces’ sudden application affect the system's motion?

Challenge and get performance evaluation