Critical damping will occur when

                          [       2          b^2    ]
        omega   =    sqrt [  omega     -  -------   ]   =   0
                          [       0        4 * m^2  ]

so 

        b   =   2 * m * omega    =  2 * (2 kg) * (4 rad/s)  =  16 kg/s
                             0