A$)$ Explain what is meant by static and dynamic coupling of multi degree of freedom systems. And discuss the ways in which the equations can be decoupled. For the $2$ Degree of freedom model, shown in figure $2,$ the normal modes are given by ${}_1=(\frac{0\mathrm{.}5}{1})$ and ${}_2=(\frac{-1}{1}).$ Write the governing equation and represent it as two de coupled single degree of freedom equation.

$(12$ marks$)$

Figure $2$