13.8 - Examples and Case Studies
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Practice Questions
Test your understanding with targeted questions
What defines a two-degree-of-freedom system?
💡 Hint: Think of how many ways it can move.
What are participation factors?
💡 Hint: They help understand the importance of modes in vibration.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the significance of natural frequencies in a system?
💡 Hint: Consider the frequency at which the system will vibrate the most efficiently.
True or False: In a two-degree-of-freedom system, both modes can oscillate independently.
💡 Hint: Remember the definition of two degrees of freedom.
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Challenge Problems
Push your limits with advanced challenges
A two-degree-of-freedom system has a mass matrix M = [[2, 0], [0, 3]] and a stiffness matrix K = [[6, -2], [-2, 5]]. Calculate the natural frequencies.
💡 Hint: Use the determinant to create your characteristic equation.
For a three-storey shear building, explain how you would determine which modes are significant for seismic analysis and how you would approach the modal validation.
💡 Hint: Look at how much each mode contributes to the overall movement.
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Reference links
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