15.2 - Mathematical Formulation of Mode Shapes
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Practice Questions
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What does the mass matrix [M] represent?
💡 Hint: Think about how mass affects motion.
What is a mode shape?
💡 Hint: It often changes during vibrations.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does the mass matrix [M] contain?
💡 Hint: Remember what mass contributes to motion.
True or False: The eigenvalue problem helps engineers calculate the stiffness of a structure.
💡 Hint: Think about what information helps in structure analysis.
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Challenge Problems
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Given a simple MDOF system with a mass ratio of 2:1, derive the eigenvalues and mode shapes.
💡 Hint: Think of how mass ratios affect frequency.
Examine a structure with uneven mass distribution and predict how it will affect its mode shapes.
💡 Hint: Consider examples of structures you've learned about.
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