When ${}_1,{}_2$ and ${}_3$ are small angles, the mechanical system on the right

can be modelled using the equation $M{x}^{}+Kx=0_{31},$ where $Min{R}^{33},$

$Kin{R}^{33}$ and $x=\left[\begin{array}{c}{}_1\\ {}_2\\ {}_3\end{array}\right]in{R}^3.$ Which of the following can be the

response of $x$ to some initial conditions, given that $M^{-1}K=$

$\frac{1}{3}\left[\begin{array}{ccc}1& -1& -1\\ 1& 0& -1\\ 1& 1& 2\end{array}\right]\left[\begin{array}{ccc}4& 0& 0\\ 0& 9& 0\\ 0& 0& 16\end{array}\right]\left[\begin{array}{ccc}1& 1& 1\\ -3& 3& 0\\ 1& -2& 1\end{array}\right]?$

A: ${}_1(t)$

A: ${}_2(t)$

A: ${}_3(t)$

B: ${}_1(t)$

B: ${}_2(t)$

B: ${}_3(t)$

C: ${}_1(t)$

C: ${}_2(t)$

C: ${}_3(t)$