12.2 - Free Vibration of Undamped 2-DOF Systems
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Practice Questions
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What does a two degree of freedom system represent?
💡 Hint: Think about how many directions or movements it can describe.
Write down the general form of the equation of motion for mass m1.
💡 Hint: Remember it includes forces and acceleration terms.
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Interactive Quizzes
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What does 'M' represent in the equation Mx'' + Kx = 0?
💡 Hint: It’s where we account for inertia.
True or False: Coupling stiffness is not important in a 2-DOF system.
💡 Hint: Think about how one mass affects the other during vibrations.
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Challenge Problems
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Consider an undamped 2-DOF system with m1 = 500 kg, m2 = 700 kg, k1 = 30000 N/m, k2 = 25000 N/m, and k12 = 5000 N/m. Derive the equations of motion for this system.
💡 Hint: Use the definitions of mass and spring forces relevant to each mass.
Using the derived equations for the 2-DOF system, determine the natural frequencies using appropriate methods (assume a linear approach).
💡 Hint: Remember the eigenvalue problem relates back to the determinant of (K - ω²M).
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