Practice Application Scenarios (1.7) - Topic 3: First Shifting Theorem

Practise this section

8 questions

Flashcard drill
3 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.
Find the Laplace Transform of e^3t * cos(5t).
Show hintHide hint
Start with the transform of cos(bt).
Question 2.
What shift do we apply for e^{-2t} f(t)?
Show hintHide hint
Remember the sign when applying the shift.
3Question 3.
What is the result of applying the First Shifting Theorem to e^{2t} * sin(3t)?
- s^2 + 9
- (s-2)^2 + 9
- (s+2)^2 + 9
Show hintHide hint
Remember the shift rule defined by the theorem.
4Question 4.
True or False: The conditions s > Re(a) must be met when applying the First Shifting Theorem.
- True
- False
Show hintHide hint
Think about the nature of the exponentials involved.
Question 5.
Using the First Shifting Theorem, compute the Laplace Transform of e^{-2t}cos(6t).
Show hintHide hint
What is the standard Laplace Transform for cos(bt)?
Question 6.
Explain how the presence of e^{4t} affects the stability of the system modeled by the equation.
Show hintHide hint
Consider the implications of shifting the transform.

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