A precision grinding machine (Fig. 3.53) is supported on an isolator that has a stiffness of \(1 \mathrm{MN} / \mathrm{m}\) and a viscous damping constant of \(1 \mathrm{kN}-\mathrm{s} / \mathrm{m}\). The floor on which the machine is mounted is subjected to a harmonic disturbance due to the operation of an unbalanced engine in the vicinity of the grinding machine. Find the maximum acceptable displacement amplitude of the floor if the resulting amplitude of vibration of the grinding wheel is to be restricted to \(10^{-6} \mathrm{~m}\). Assume that the grinding machine and the wheel are a rigid body of weight \(5000 \mathrm{~N}\).

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Grinding machine Grinding wheel x(t) Isolator Floor FIGURE 3.53 Grinding machine on isolator. y(t) = Y sin col = Y sin 200 at m