16.4 - Free Vibration of Undamped MDOF Systems
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Practice Questions
Test your understanding with targeted questions
What is natural frequency?
💡 Hint: Think about how a swing oscillates.
Define mode shape.
💡 Hint: Consider how various points of a structure move together.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does ω² represent in the context of MDOF systems?
💡 Hint: Think about the vibrations of the system.
Mode shapes are orthogonal to mass and stiffness matrices. True or False?
💡 Hint: What does orthogonality imply about two vectors?
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Challenge Problems
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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.
💡 Hint: Solve the characteristic equation.
Discuss how the eigenvalue analysis of an MDOF system with two degrees of freedom differs from that of a single-degree system.
💡 Hint: Consider the differences in analysis approaches.
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