Practice Time-Shift for General Function - 9.1.5.2 | 9. Laplace Transform of Unit Step Function | Mathematics - iii (Differential Calculus) - Vol 1
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Time-Shift for General Function

9.1.5.2 - Time-Shift for General Function

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Learning

Practice Questions

Test your understanding with targeted questions

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.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

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.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

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.

Challenge 2 Hard

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?

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