$8/91$ The two masses are connected by an inextensible cable which passes securely over the periphery of the cylindrical pulley of mass $m_3,$ radius $r,$ and radius of gyration $k_O.$ Determine the equation of motion for the system in terms of the variable $x.$ State the critical driving frequency ${}_c$ of the block $B$ which will result in excessively large oscillations of the assembly. Evaluate for $m_1=25kg,m_2=10kg,m_3=15kg,k_1=450\frac{N}{m},k_2=300\frac{N}{m},r=300mm,$ and $k_O=200mm.$

$x_n=$bsin$t$