17.9 - Eigenvalues and Modes of Vibration
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Practice Questions
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What is an eigenvalue?
💡 Hint: Think about linear transformations.
Define natural mode.
💡 Hint: Relate it to oscillations in a string.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the relationship between eigenvalues and natural frequency?
💡 Hint: Think about the mathematical representation.
True or false: Resonance occurs when operational frequencies match natural frequencies.
💡 Hint: Consider the implications of this in engineering.
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Challenge Problems
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Given a fixed beam of length L, calculate its first three eigenvalues and corresponding natural frequencies.
💡 Hint: Use the formula for eigenvalues and substitute n = 1, 2, 3.
Discuss the implications of resonance in the design of tall buildings under seismic activity.
💡 Hint: Consider examples from engineering practices.
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