Problem $2$

At the instant shown, the $1\mathrm{.}5$ kg bar rotates clockwise at $\backslash (2\backslash$mathrm$\{$rad$\}/\backslash$mathrm$\{$s$\}\backslash ).$ The spring attached to its end always remains vertical due to the roller guide at $\backslash ($ C $\backslash ).$ If the spring has an unstretched length of $2$ m and a stiffness of $\backslash (\backslash$mathrm$\{$k$\}=6\backslash$mathrm$\{$~N$\}/\backslash$mathrm$\{$m$\}\backslash ),$ determine the angular velocity of the bar the instant it has rotated $\backslash (30^\{\backslash$circ$\}\backslash )$ clockwise.