12.3 - Natural Frequencies and Mode Shapes
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Practice Questions
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What is a natural frequency?
💡 Hint: Think about the default rhythm of a system.
Define mode shape.
💡 Hint: Consider it as how different parts of a system move together.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the eigenvalue problem formed from the motion equation?
💡 Hint: Look for the determinant condition.
Natural frequencies directly relate to which concept?
💡 Hint: Think about how vibrations are influenced.
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Challenge Problems
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Consider a 2-DOF system defined with masses M1 and M2, find the natural frequencies if the stiffness matrix is given as K = [[30000, -10000], [-10000, 30000]].
💡 Hint: Start by calculating the determinant for potential ω values.
Discuss how changing the stiffness of one mass affects the mode shapes of this 2-DOF system.
💡 Hint: Consider how frequency shifts impact vibration patterns.
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