A frame is shown in Figure $3.$ Beam CD is risid and the total mass of the rigid beam is

m$.$ All columns are massless and all with stiffiness EI$.$ A mass m is fixed on top E of

column CE$.$ There is a horizontal dynamic load $f(t)=4sint(kV)$ acting on $CD.$

$3\mathrm{.}1)$ Determine the natural frequencies and corresponding mode shapes.

$3\mathrm{.}2)$ Redesign column CE and the mass on top E to make this part work as a DAV

$3\mathrm{.}3)$ Determine the amplitude of $CD$ and the amplitude of the new mass on E under the

dynamic load after your redesign in $3\mathrm{.}2)$