$(4)$ Rolling wheel with spring, pulley and block

Uniform disk wheel has radius $r,$ mass $m_2,$ rotation $(t)($not small angle$),$ spring constant $k$

and block mass $m_1,$ small pulleys have no mass, spring and cable attached to the hub of rolling

wheel, block position $x(t)$ and wheel position $y(t)$ are all zero when spring is at resting length.

Find the single equation of motion of the system in terms of $x(t).$