A one story building, with a mass equal $(519\mathrm{.}8/4*103)$ kg idealized as a $4-$m high frame with two column hinged at the base and rigid beam, Each column is a European standard steel IPE $220.$ Its properties for bending about its major axis are Ix$=2772$ cm$4,$ E$=200,000$ Mpa, If damping ratio is $\backslash$xi $=0\mathrm{.}125$

a$)$ Find the response when two equal impulses of $(519\mathrm{.}8/2)$ kN are applied $5$ seconds apart. $($Write the equation of motion up to $20$ seconds$)$

b$)$ Find the moments in the column at $4$ seconds

c$)$ Find the moment in the column at $10$ seconds