PROBLEM $2\mathrm{.}2(20$ Points$)$ You are to design a cantilever$-$beam$-$type seismic transducer to measure the displacement of a vibrating structure. The transducer must have a displacement amplitude error within $+-2\%$ for all input frequencies in the range $10-100Hz.$ You have selected a $0\mathrm{.}5-kg$ seismic mass. Assuming that the damping ratio is $0\mathrm{.}15,$ determine an appropriate range for the beam stiffness $($in $\frac{N}{m}).$