A two$-$degree$-$of$-$freedom mechanical system with five springs and two masses is shown in the Fig., and $F_1$ and $F_2$ are exciting force respectively. Please determine: $(1)$ The equation of motion; $(2)$ The natural frequencies; $(3)$ The modal vectors and to draw the modal vector curves. $($ Note: values of $k,m$ equal to your class number$).$

$k=m=4$