$($c$)$ Figure $3($Q$2)$ shows a dynamic model of a two floor shear structure type building. The

masses $m_1$ and $m_2$ represent the floors of the building while the beams of stiffnesses $k$ and

$2k$ support the floors and provide lateral stiffness. Derive the equations of motion of the

system for lateral motion and write them down in matrix form.

$[8$ marks$]$

Figure $3($Q$2)$