A machine of \(100 \mathrm{~kg}\) mass has a \(20 \mathrm{~kg}\) rotor with \(0.5 \mathrm{~mm}\) eccentricity. The mounting springs have stiffness \(85 \mathrm{kN} / \mathrm{m}\) and damping is negligible. If the operating speed is \(20 \pi \mathrm{rad} / \mathrm{s}\) and the unit is constrained to move vertically, the dynamic amplitude of the machine will be

(a) \(0.470 \times 10^{-4} \mathrm{~m}\)

(b) \(1.000 \times 10^{-4} \mathrm{~m}\)

(c) \(1.270 \times 10^{-4} \mathrm{~m}\)

(d) \(2.540 \times 10^{-4} \mathrm{~m}\).