A frame structure is shown in Figure $3.$ All the columns have same EI$.F(t)=20sint(KN)$

Determine the natural frequencies and corresponding mode shapes

Loading frequency is $=1\mathrm{.}25\frac{EI}{h^3},$ do we have the risk of resonance?

Re$-$design the top storey to make it a tuned mass damper

Set up the equations of motion of the structure under $F(t)$ and earthquake: ground

displacement $x_g=0\mathrm{.}02sin56t(m)$

Figure $3$