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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What does orthogonality in mode shapes indicate?
💡 Hint: Think about how angles relate to each other.
Question 2
Easy
Name one reason for normalizing mode shapes.
💡 Hint: How can we measure contributions fairly?
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 orthogonality condition for mode shapes with respect to the mass matrix?
- {ϕ}T[M]{ϕ} = 1 for i = j
- {ϕ}T[M]{ϕ} = 0 for i ≠ j
- {ϕ}T[M]{ϕ} = ω²
💡 Hint: Think about how interactions could complicate motion.
Question 2
True or False: Normalization makes mode shapes unique in magnitude.
- True
- False
💡 Hint: Consider if different modes could still exist in varying sizes.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
A three-story shear building shows interference between the first two mode shapes during an earthquake simulation. Discuss the potential implications and propose adjustments.
💡 Hint: Reflect on the significance of independent modes.
Question 2
Consider a structure with two normalized mode shapes. If one mode shape contributes significantly more than the other during an analysis, how would you interpret this in terms of design?
💡 Hint: Think about how mode shapes influence stress on materials.
Challenge and get performance evaluation