$4(25\%)-$ For the two story$-$building shown $($Figure P$-4),$ determine frequencies and mode shapes $($assume unity for second DOF$/$floor$).$ Note differences in stiffness, $k,$ and mass, $m,$ of each floor$/$story$.$ When $k=100$kip$\frac{s}{i}n$ and the frequency of the applied loads is equal to $85\%$ of ${}_1$ the maximum modal responses are equal to $2\mathrm{.}0$ and $0\mathrm{.}02$ in the first and second mode, respectively. Determine the amplitude of the exciting forces $($i$.$e$.,F_1$ and $F_2)?$

Figure $P-2$

${}_1=3\mathrm{.}750\sqrt[\phantom{2}]{E\frac{\text{I}}{m}{h}^3}$

First mode

${}_2=9\mathrm{.}052\sqrt[\phantom{2}]{E\frac{\text{I}}{m^3}}$

Second mode

$\frac{m}{2}$