Practice Examples (1.8) - Second Shifting Theorem - Mathematics - iii (Differential Calculus)

Practise this section

9 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
3 questions · about 2 min · pass mark 70%. Hints available.
Sign up to start the quiz

6 sample questions

Question 1.
Define the Heaviside step function.
Show hintHide hint
Consider how the function behaves over different time intervals.
Question 2.
What does the Second Shifting Theorem state?
Show hintHide hint
Recall the notation and the meaning of each variable.
3Question 3.
What is the equation for the Second Shifting Theorem?
- ℒ{f(t-a)u_a(t)} = e^{-as}F(s)
- ℒ{f(t+a)u_a(t)} = e^{as}F(s)
- ℒ{f(t)u_a(t)} = F(s)
Show hintHide hint
Focus on the role of the negative exponent.
4Question 4.
True or False: The Heaviside function is zero for all time.
- True
- False
Show hintHide hint
Consider when it activates.
Question 5.
What is the Laplace transform of (t-3)^3u_3(t)? Provide a detailed solution.
Show hintHide hint
Remember to find the initial Laplace transform of t^3.
Question 6.
Consider a system where the response to an input signal starts after a delay of 5 seconds. How would you mathematically represent the output in terms of the Second Shifting Theorem?
Show hintHide hint
Think about how time delays linearly translate in the Laplace domain.

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