An inextensible cable is attached to a fixed support, wraps around the periphery of a disc of mass $2$m kg and radius r m and is attached to a spring of stiffness k N$/$m$,$ which is also attached to the fixed support. A suspended block B of mass m kg is attached to the centre of the disc, A$,$ by means of a massless, inextensible cable. The system is initially at rest when a moment M Nm CCW acts on the disc. The cabledoesnotsliponthedisc. $($a$)$Ifm$=10$kg$,$r$=0\mathrm{.}2$ m$,$ k $=250$ N$/$m$,$ determine the initial stretch s$1$ m in the spring at static equilibrium $($before the moment is applied$)[2$ marks$].($b$)$ Ignore your answer and assume the fictitious value s$1=0\mathrm{.}5$ m$.$ Set y and to zero at the static equi$-$ librium position and consider the motion when a moment M $=40$ Nm is now applied to the disc. Determine the trans$-$ lational velocity of the suspended block, vB$,$ when y $=0\mathrm{.}3$ m $[8$ marks$].$