Practice Heaviside’s Expansion Formula (for Distinct Poles) (12.3.4) - Inverse Laplace Transform

Practice: Heaviside’s Expansion Formula (for distinct poles)

Lesson 12.3.4Inverse Laplace Transform

Practise this section

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

6 sample questions

Question 1.
Identify the poles of F(s) = (5s + 10) / (s^2 - 5s + 6).
Show hintHide hint
Set the denominator equal to zero and solve for 's'.
Question 2.
What does the term P(a_i) represent in Heaviside's formula?
Show hintHide hint
Think of it as the output of the polynomial when you substitute the pole.
3Question 3.
What does Heaviside's Expansion Formula help calculate?
- Direct Laplace Transform
- Inverse Laplace Transform
- Fourier Transform
Show hintHide hint
Think about the function we retrieve from the frequency domain.
4Question 4.
If F(s) = (3s + 4) / ((s - 1)(s - 2)), what are the poles?
Show hintHide hint
Factor the denominator to find the roots.
Question 5.
Using Heaviside's expansion, derive the inverse Laplace transform of F(s) = (2s + 3) / ((s - 1)(s - 2)^2). Consider both poles in your solution.
Show hintHide hint
Remember to account for the double pole by differentiating.
Question 6.
Explain why Heaviside's formula is not applicable to rational functions with non-distinct poles. Create an example to illustrate your point.
Show hintHide hint
Reflect on how distinct effects help simplify.

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