Practice General Form Of Second-order Linear Differential Equations (4.1) - Case of Complex Roots

Practice: General Form of Second-Order Linear Differential Equations

Lesson 4.1Case of Complex Roots

Practise this section

8 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
2 questions · about 1 min · pass mark 70%. Hints available.
Sign up to start the quiz

6 sample questions

Question 1.
What is the general form of a second-order linear differential equation?
Show hintHide hint
Look for terms involving second and first derivatives.
Question 2.
What does the discriminant signify in the characteristic equation?
Show hintHide hint
Recall the formula for the discriminant \$ D = b^2 - 4ac \$.
3Question 3.
What is the characteristic equation for a second-order linear differential equation?
- ar^2 + br + c = 0
- y'' + by' + cy = 0
- dy/dx = mx + b
Show hintHide hint
Look for the basic structure of a quadratic equation.
4Question 4.
True or False: Complex roots suggest oscillatory behavior.
- True
- False
Show hintHide hint
Think about how motion resembles a wave.
Question 5.
A damper's characteristics are described by $j \frac{d^2y}{dt^2} + k\frac{dy}{dt} + m y = 0$ . If j = 1 kg, k = 50 Ns/m, m = 10 N/m, compute the roots and describe the motion.
Show hintHide hint
Check the discriminant for nature of the roots.
Question 6.
In a dynamic analysis of a bridge, if the displacement gives you $5 \frac{d^2y}{dx^2} + 40\frac{dy}{dx} + 100y = 0$ , find the characteristic roots and their implications.
Show hintHide hint
Remember: D < 0 indicates complex roots!

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