Identify the equation of motion for the system shown in this figure. Discount the mass of the L$-$shaped arm. The gravity is pointing down. Select the coordinate system origin $)=(0$ as the static equilibrium and consider a small amplitude of motion.

$m{D}_2^2{x}^{}=-k{D}_1^{2}x$

None of the above

$m{D}_1^2{x}^{}=-k{D}_2^{2}x$

$m{D}_1^2{x}^{}=k{D}_2^{2}x$

$m{D}_2^2{x}^{}=k{D}_1^{2}x$