It is proposed to build a \(6-\mathrm{m}\) smokestack on the top of a \(60-\mathrm{m}\) factory. The smokestack will be made of steel \(\left(ho=7850 \mathrm{~kg} / \mathrm{m}^{3}\right)\) and will have an inner radius of \(40 \mathrm{~cm}\) and an outer radius of \(45 \mathrm{~cm}\). What is the maximum amplitude of vibration due to vortex shedding and at what wind speed will it occur? Use a SDOF model for the smokestack with a concentrated mass at its end to account for inertia effects. Use \(\zeta=0.05\).