A compressor of 45 kg operates at variable speeds from 900 to 1750 rpm. Mounted on the roof of a room, the compressor generates a harmonic force of constant amplitude, transmitted to the roof and causes its vibration. If no isolation is used between the motor and the roof, the noise radiated by the vibrating roof towards the room exceeds the required level by 12dB. A vibration isolator is therefore envisaged to be used to attenuate the force transmission, which will subsequently lead to a noise reduction inside the room. (a) What is the transmissibility required to reduce the noise by 12 dB? (b) By neglecting damping, determine the stiffness of the isolator to achieve the isolation needed. (c) In practice, damping always exists. In that case, is the effective noise reduction higher or lower than 12 dB? Explain why? If a softer isolator is used, in which way the isolation performance would be affected? (d)