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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define eigenvalue and give an example.
💡 Hint: Think about the formula mentioned in class.
Question 2
Easy
Explain the relationship between eigenvalues and eigenfunctions.
💡 Hint: Consider the definitions you learned.
Practice 1 more question 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 formula for the eigenvalue α?
- α = nπ/a
- α = mπ/b
- α = n * m
💡 Hint: Look for the formula mentioned in class.
Question 2
True or False: Eigenfunctions describe the boundary conditions of the system.
- True
- False
💡 Hint: Think about what each term represents.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
A rectangular membrane has a length of 2m and a width of 1m. Calculate the first three eigenvalues.
💡 Hint: Use the formulas for α and β.
Question 2
If the initial displacement of a vibrating membrane is given by the function f(x,y) = sin(πx/2)sin(πy), identify the corresponding eigenvalue pairs.
💡 Hint: What values of n and m fit the given function?
Challenge and get performance evaluation