The signpost of a fast food restaurant consists of a hollow steel cylinder of height \(h\), inside diameter \(d\), and outside diameter \(D\), fixed to the ground and carries a concentrated mass \(M\) at the top. It can be modeled as a single-degree-of-freedom spring-mass-damper system with an equivalent viscous-damping ratio of 0.1 for analyzing its transverse vibration characteristics under wind excitation. Determine the following:

(a) the natural frequency of transverse vibration of the signpost;

(b) the wind velocity at which the signpost undergoes maximum steady-state displacement; and

(c) the maximum wind-induced steady-state displacement of the signpost. Data: \(h=10 \mathrm{~m}, D=25 \mathrm{~cm}, d=20 \mathrm{~cm}, M=200 \mathrm{~kg}\).