Practice Partial Fraction Method (12.3.1) - Inverse Laplace Transform - Mathematics - iii (Differential Calculus) - Vol 1

Practice: Partial Fraction Method

Lesson 12.3.1Inverse Laplace Transform

Practise this section

10 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
4 questions · about 3 min · pass mark 70%. Hints available.
Sign up to start the quiz

6 sample questions

Question 1.
Express $F(s) = \frac{1}{s^2 + 3s + 2}$ in partial fractions.
Show hintHide hint
Set up the equation and equate coefficients for A and B.
Question 2.
What is the first step in using the Partial Fraction Method?
Show hintHide hint
Remember, a rational function needs to be simplified.
3Question 3.
What is the first step in the Partial Fraction Method?
- Express F(s)
- Multiplying by the denominator
- Finding coefficients
Show hintHide hint
Think about what needs to be done before we can simplify.
4Question 4.
True or False: The partial fraction method can only be used for proper rational functions.
- True
- False
Show hintHide hint
Consider the definitions of proper and improper fractions.
Question 5.
Determine the inverse Laplace transform of $F(s) = \frac{5s^2 + 4s + 3}{(s + 1)(s^2 + 4s + 4)}$ using partial fractions.
Show hintHide hint
Remember to factor the quadratic in the denominator for easier decomposition.
Question 6.
Discuss the significance of partial fractions in dynamic systems simulation.
Show hintHide hint
Think about how ease of computation impacts system design and analysis.

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