Consider the system in FigureP4.4. FigureP4.4 a. Derive the differential equations of motion and obtain the mass

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Consider the system in FigureP4.4.

FigureP4.4 

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a. Derive the differential equations of motion and obtain the mass and stiffness matrices.

b. Calculate the natural frequencies and the mode shapes.

c. Find the initial conditions such that the free vibration is sinusoidal with each natural frequency.

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