16.14 - Numerical Example: 2-DOF System
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Practice Questions
Test your understanding with targeted questions
Define the mass matrix for a 2-DOF system with m1=5 kg, m2=10 kg.
💡 Hint: Consider how mass is represented in matrix form.
What does the stiffness matrix represent?
💡 Hint: Think about the properties of the materials involved.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does the mass matrix in a 2-DOF system represent?
💡 Hint: Consider what defines the motion of each mass.
Is the stiffness matrix in a 2-DOF system always symmetric?
💡 Hint: Think about how stiffness in structures interacts.
1 more question available
Challenge Problems
Push your limits with advanced challenges
Consider a 2-DOF system with masses m1=12 kg and m2=8 kg. The stiffness matrix is given as [K] = [[30, -10], [-10, 20]]. Calculate the natural frequencies and corresponding mode shapes.
💡 Hint: Use MATLAB or numerical methods for precise calculations.
For the 2-DOF system, determine the response to an external seismic input defined by a force vector. Use modal superposition to articulate the total displacement.
💡 Hint: Break down each mode's impact and ensure correct summation.
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