Practice Time-shift For General Function (9.1.5.2) - Laplace Transform of Unit Step Function

Practice: Time-Shift for General Function

Lesson 9.1.5.2Laplace Transform of Unit Step Function

Practise this section

8 questions

Flashcard drill
4 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
Sign up to start the exercise
Quiz
2 questions · about 1 min · pass mark 70%. Hints available.
Sign up to start the quiz

6 sample questions

Question 1.
What defines the unit step function?
Show hintHide hint
Think about what happens at the jump point.
Question 2.
Write the Laplace Transform of u(t-a).
Show hintHide hint
Look for the exponential function in the formula.
3Question 3.
What is the unit step function?
- A function that oscillates.
- A function that stays constant.
- A function that jumps at a specific point.
Show hintHide hint
Focus on the defining feature of the function.
4Question 4.
True or False: The Laplace Transform is used to convert functions from the frequency domain to time domain.
- True
- False
Show hintHide hint
Remember the direction of the transform.
Question 5.
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.
Show hintHide hint
Start by writing down what happens at the time 3 seconds.
Question 6.
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.
Show hintHide hint
How does the forces’ sudden application affect the system's motion?

4 more questions in this section. Enroll free to practise them all.