A frame structure is shown in Figure $3.$ A dynamic load $F(t)$ acting on the roof as shown. Assume that all the slabs are rigid and all columns are massless.

CIVN$7005$ EXAM$-2014$

$3\mathrm{.}1)$ Develop the equations of motion for the system $($ under load $F(t))$

$3\mathrm{.}2)$ Determine the natural frequencies of the system

$3\mathrm{.}3)$ Scktch the corresponding mode shapes

$3\mathrm{.}4)$ Besides load $F(t),$ the structure now experience an earthquake, the acceleration at the foundation is $a=0\mathrm{.}5$gsin$(t).$ Set up the equation of eauation for this case.