A hollow steel shaft of length \(2.6 \mathrm{~m}\), outer diameter \(110 \mathrm{~mm}\), and inner diameter \(95 \mathrm{~mm}\), carries the rotor of a turbine, of mass \(250 \mathrm{~kg}\), at the middle and is supported at the ends in bearings. The clearance between the rotor and the stator is \(12 \mathrm{~mm}\). The rotor has an eccentricity equivalent to a weight of \(0.25 \mathrm{~kg}\) at a radius of \(45 \mathrm{~mm}\). A limit switch is installed to stop the rotor whenever the rotor touches the stator. If the rotor operates at resonance, how long will it take to activate the limit switch? Assume the initial displacement and velocity of the rotor perpendicular to the shaft to be zero.