As the light rod rotates about point $0,$ it carries a mass point of $2$ kg and a mass of $4$ kg$,$ respectively. When the rod starts to move from rest at a position of $0=60\backslash$deg and rotates on a vertical plane, find $($a$)$ the velocity v immediately before the spring is struck at the position where the mass of $2$ kg is dotted. $($b$)$ Find the maximum compression displacement x of the spring. Since the value of x is so small, when the spring is compressed, it is assumed that the position of the rod is horizontal.