for the one$-$bay one story frame $)=(h,$ ignore the shear deformation and use $x(t)$ as the coordinate to define the vibration response of the structure. Assume the structure has viscous damping ratio of $=5\%,$ and $I_b=0\mathrm{.}6I_c.$ use the Newmark method with constant average acceleration

a$)$ Use the flexibility method to derive the lateral stiffness of the frame.

b$)$ For the explosive force with finite duration $t_d,$ as shown below with $$ equal to $\frac{1}{5},$ calculate the response spectrum for the maximum displacement of $x(t).$

c$)$ For the explosive force with finite duration $t_d,$ as shown below with $$ equal to $\frac{1}{5},$ calculate the response spectrum for the maximum of moment $M_{BA}.$

d$)$ Based on your derived response spectrum in part $b$ and assume that $t_d=0\mathrm{.}1sec,$ select the most economical W$-$sections for the beam and columns so that the value of $R_{{?}_{?}}(d)$ is less than $2\mathrm{.}0.$

Notes:

Please use MATLAB or Python to develop the response spectrum;

Notice that the SDOF system has damping; provide the complete answer from starting