A billboard assembled system is simplified as illustrated in fig. 1 in order to analyze the response of the billboard. The inertia of the pulley holding the board is I0 = 6.25 × 10-3 kgm2 and mass m = 200 kg. Spring stiffness k1 and k2 are 20 kN and 200 kN respectively. Meanwhile inner radius, r = 0.05 m.
Task A
Based on this specification,
i. Calculate and express the equation of motion of this system,
ii. Evaluate its natural frequencies and mode shapes.

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