In the following Figure a system consists of a block with mass m, spring K and a damper C; is attached to the floor where the block has a vertical oscillation x(t), and floor is vibrating vertically y(t) at 30 Hz. 1) For the case which system damping ratio is zero, what should be the natural frequency of the block vibration in order to reduce the relative motion of the block to floor by 12 dB. [2 marks] 2) If we consider a value for damper; C, which makes it equal to 10% of critical damping then what would beX/Y) ratio in this case. [1 marks] 3) Explain and justify whether adding more damping can reduce the vibration of the block in response to floor vibrating at 30 Hz [2 marks]

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