Show me the steps to solve $3\mathrm{.}1.$ A rigid plate of mass $m=400kg$ is supported by $4$ steel columns with inertia

$I=70{10}^{3}m{m}^4$ and Young's modulus $E=200000$MPa, as shown in figures $($a$)$ and $($b$)$

below. The period of the structure is $T=1\mathrm{.}0s.$ Two special braces are added, which can

dissipate energy by means of friction $(2$ sliding surfaces pressed against each other by a force

$N,$ per brace$)$ as shown in figure $($c$).$ Each brace develops an axial force of magnitude $F=N.$

The coefficient of friction is $=0\mathrm{.}75.$ Calculate the value of $N$ such that the lateral

displacement can decrease from an initial value of $10$ mm to less than $1$ mm in no more than

$6\mathrm{.}5$ s during a free vibration test. Use the Coulomb damping model, neglect any viscous

damping, and assume the added braces provide only damping $($no added stiffness$).$

a$.$ Plan view

b$.$ Section A$-$A

c$.$ Section A$-$A with diagonal friction

dampers $($undeformed$/$deformed$).$