Consider the system in Figure P4.2. Figure P4.2 a. Derive the differential equations of motion and obtain

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Consider the system in Figure P4.2.

Figure P4.2 

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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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