Practice Free Vibration Of Undamped Mdof Systems (16.4)

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9 questions

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6 sample questions

Question 1.
What is natural frequency?
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Think about how a swing oscillates.
Question 2.
Define mode shape.
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Consider how various points of a structure move together.
3Question 3.
What does ω² represent in the context of MDOF systems?
- Damping Ratio
- Eigenvalues
- Stiffness
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Think about the vibrations of the system.
4Question 4.
Mode shapes are orthogonal to mass and stiffness matrices. True or False?
- True
- False
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What does orthogonality imply about two vectors?
Question 5.
Given a system with a known mass matrix $M = [[1, 0], [0, 2]]$ and stiffness matrix $K = [[10, -5], [-5, 5]]$ , compute the eigenvalues and eigenvectors.
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Solve the characteristic equation.
Question 6.
Discuss how the eigenvalue analysis of an MDOF system with two degrees of freedom differs from that of a single-degree system.
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Consider the differences in analysis approaches.

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