The building frame structure in Fig. P$2\mathrm{.}1$ consistsof a rigid horizontal member BC of mass m supportedby two vertical columns each of whose bending stiffnessis EI$.$ Neglect the effect of the weight of BC onthe stiffness of the vertical members. $($a$)$ Determine theequation of motion of mass m$.($b$)$ How would theequation of motion differ if the left$-$hand column hada stiffness $2$EI with no other changes to the structure?

$2\mathrm{.}1$ The building frame structure in Fig. P$2\mathrm{.}1$ consists of a rigid horizontal member $BC$ of mass $m$ supported by two vertical columns each of whose bending stiffness is $EI.$ Neglect the effect of the weight of $BC$ on the stiffness of the vertical members. $($a$)$ Determine the equation of motion of mass $m.($b$)$ How would the equation of motion differ if the left$-$hand column had a stiffness $2EI$ with no other changes to the structure?

Figure P$2\mathrm{.}1$