Practice Laplace Transform Of Unit Step Function (9.1) - Laplace Transform of Unit Step Function

Practice: Laplace Transform of Unit Step Function

Lesson 9.1Laplace Transform of Unit Step Function

Practise this section

10 questions

Flashcard drill
2 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
4 questions · about 3 min · pass mark 70%. Hints available.
Sign up to start the quiz

6 sample questions

Question 1.
Define the unit step function.
Show hintHide hint
Think about how the function behaves over time.
Question 2.
What is the Laplace Transform of u(t−a)?
Show hintHide hint
Recall the formula we derived.
3Question 3.
What is the definition of the unit step function?
Show hintHide hint
Consider how the function activates.
4Question 4.
The Laplace Transform of u(t−a) is given by which formula?
- e^{−as}/s
- s/(e^{as})
- (1/s)e^{−as}
Show hintHide hint
Recall the transformation formula we discussed.
Question 5.
Consider a switch that activates at t = 3 in a system described by the function f(t) = cos(t). Calculate the Laplace Transform of the system taking into account the unit step function.
Show hintHide hint
Use the property of shifting and recognize cos(t) transforms.
Question 6.
A mechanical system experiences a sudden force at t = 4 described by the impulse m*d²x/dt² + kx = F(t)u(t−4). Derive the system response in the Laplace domain.
Show hintHide hint
Focus on the relationship established through the Laplace properties of derivatives.

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