Solve fast $.$ In the system shown in the static equilibrium position, a spring with a spring coefficient $\backslash ($ k$\_\{1\}\backslash )$ is attached to point $\backslash ($ A $\backslash ),$ and a spring with a spring coefficient $\backslash ($ k$\_\{2\}\backslash )$ is attached to point B$.$ O is the center of the mass of the homogeneous cylinder. The cylinder is rolling without slipping on the ground. An inextensible rope is wrapped around the cylinder of mass $\backslash ($ m $\backslash )$ and radius $\backslash ($ R $\backslash ).$ A mass of $\backslash ($ M $\backslash )$ is attached to the end of the rope. Obtain the equation of motion of the small amplitude vibrations of the system around the static equilibrium position by constructing the equivalent system.