15.1 - Free Vibration and Mode Shapes
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Practice Questions
Test your understanding with targeted questions
Define free vibration.
💡 Hint: Think about motion after a swing is pushed.
What corresponds to each mode shape?
💡 Hint: How many frequencies are in a multi-degree system?
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is free vibration?
💡 Hint: Think about a system left to move after being disturbed.
Each mode shape in a structure corresponds to:
💡 Hint: How many frequencies match up with each individual deformation shape?
2 more questions available
Challenge Problems
Push your limits with advanced challenges
Analyze a 4-DOF cantilever beam subjected to an initial disturbance and determine the mode shapes and corresponding natural frequencies.
💡 Hint: Consider utilizing numerical methods like Rayleigh-Ritz for complex structures.
In the design of a new building, how would you mitigate the effects of resonance identified from mode shapes?
Consider the material properties and structural reinforcement strategies.
💡 Hint: Think about how materials can affect vibrations in a structure.
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