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3 cards from this section. Quick, good the night before a test.
What does a two degree of freedom system represent?
Think about how many directions or movements it can describe.
Write down the general form of the equation of motion for mass m1.
Remember it includes forces and acceleration terms.
What does 'M' represent in the equation Mx'' + Kx = 0?
It’s where we account for inertia.
True or False: Coupling stiffness is not important in a 2-DOF system.
Think about how one mass affects the other during vibrations.
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.
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).
Remember the eigenvalue problem relates back to the determinant of (K - ω²M).
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