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Lagrange Method in Mechanical Vibration

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Advanced dynamics. See attached file for full problem description.

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Solution to a mechanical vibration can be obtained using several ways. One of them is by considering a energy conservation in the system when no energy losses such as friction is present in the system. this is named as "Lagrange's method". When the system is complicated it is difficult to analyse part by part and find the natural frequency. This method solves that problem.

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Mechanical Vibration

The machine shown in the figure is rigidly anchored on a rigid concrete block and the mass of both is 3000 kg. The block has height h = 1 m and square horizontal section with a = 1.2 m and is supported at the corners by 12 springs of stiffness k = 2000 N/m.

Solve only the second part: (see attachment for diagram)
ii) Find the natural frequencies and mode shapes of the system using both hand calculations and Matlab.

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