A bridge is modelled as a system with a single degree of freedom, as shown in the figure. The

bridge has a mass of $16000{10}^{3}kg$ and a natural frequency of $4\mathrm{.}9$ Hz $.$ Under the action of a

vehicle that produces a harmonic force of $6,167N,$ the bridge undergoes excessive vibration. If it is

decided to use an undamped vibration absorber of mass $3,626kg$ in order to suppress the bridge's

vibration at its fundamental natural frequency, determine the maximum amplitude of vibration of the

absorber$.$ Give your answer in mm $.$ Work to $3$ decimal places.