11.3 - Mode Shapes and Natural Frequencies
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Practice Questions
Test your understanding with targeted questions
Define natural frequency in your own words.
💡 Hint: Think about how tuning forks resonate.
What are mode shapes?
💡 Hint: Consider how different instruments vibrate.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What defines the natural frequencies of a system?
💡 Hint: Consider what properties influence oscillation.
True or False: Mode shapes can interfere with each other.
💡 Hint: Think about independence in terms of vectors.
1 more question available
Challenge Problems
Push your limits with advanced challenges
Given a two-mass spring system, derive the natural frequencies and mode shapes of the system. Consider both masses and springs in your analysis.
💡 Hint: Make use of the symmetry in the eigenvalue problem.
In a multi-storey building, discuss how mode shapes affect the building's response to seismic activity, providing specific examples.
💡 Hint: Consider how the distribution of mass can modify the force spread during an earthquake.
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