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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Solve the equation d²y + 6dy + 10y = 0.
💡 Hint: Use the quadratic formula to find the roots.
Question 2
Easy
What does a negative discriminant indicate in a differential equation?
💡 Hint: Recall the discriminant formula D = b² - 4ac.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What is the characteristic equation for the differential equation d²y + 4dy + 13y = 0?
- r² + 4r + 13 = 0
- r² - 4r + 13 = 0
- r² + 4r - 13 = 0
💡 Hint: Recall the format of the general second-order linear differential equations.
Question 2
True or False: A negative discriminant indicates real and distinct roots.
- True
- False
💡 Hint: Think about the relationship between the discriminant and the nature of the roots.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
A suspension bridge experiences oscillations when wind blows towards it. If the governing equation is d²y/dt² + 8dy/dt + 16y = 0, analyze the system by finding the roots and assessing stability.
💡 Hint: Use the characteristic equation to derive the roots and analyze their real part.
Question 2
For a damped harmonic oscillator with a mass of 3 kg, damping coefficient of 6 Ns/m, and spring constant of 75 N/m, calculate the damping ratio ζ and natural frequency ω_n.
💡 Hint: Use the formulas for ν and rooftop damping calculations.
Challenge and get performance evaluation