Practice Unit 1: Laplace Transforms & Applications (1) - Topic 3: First Shifting Theorem

Practice: Unit 1: Laplace Transforms & Applications

Lesson 1Topic 3: First Shifting Theorem

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.
What is the First Shifting Theorem?
Show hintHide hint
Think about how an exponential affects the transform.
Question 2.
Provide the condition needed for the First Shifting Theorem to hold.
Show hintHide hint
Consider what the Laplace Transform needs to work.
3Question 3.
What does the First Shifting Theorem indicate?
- It results in a vertical shift
- It results in a horizontal shift
- It has no effect
Show hintHide hint
Review what happens when functions are modified.
4Question 4.
True or False: The Laplace Transform of $e^{-at}f(t)$ results in $F(s + a)$ .
- True
- False
Show hintHide hint
Recollect the shifting directions.
Question 5.
Find the Laplace Transform of $e^{2t} ext{cos}(3t)$ and explain your steps.
Show hintHide hint
Start from the basic Laplace transform of cos.
Question 6.
A function $f(t) = t^3$ is affected by an exponential decay $e^{-kt}$ . Determine the Laplace transform of this entire function.
Show hintHide hint
Recall the shifts and how the multipliers affect the base function.

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