(Solved): A machine of mass 200kg is mounted on the middle of a fixed-fixed beam, with a viscous damping me ...

A machine of mass $200\mathrm{kg}$ is mounted on the middle of a fixed-fixed beam, with a viscous damping mechanism not shown. The steel beam $(E=207\mathrm{GPa})$ has the following dimensions: $a=0.05\mathrm{m},\mathrm{b}=0.2\mathrm{m}$ and $\mathrm{L}=4\mathrm{m}$. It has been observed that when a harmonic force of magnitude $1000\mathrm{N}$ is applied, the maximum steady-state response occurred at a frequency of $720\mathrm{rpm}$. Determine the equivalent damping constant, neglecting the mass of the beam. $I=\frac{a^{3}b}{12}$ $9129\mathrm{Ns}/\mathrm{m}$ $6807\mathrm{Ns}/\mathrm{m}$ $7007\mathrm{Ns}/\mathrm{m}$ $7919\mathrm{s}/\mathrm{m}$