A four$-$pole, $208$ V$,60$ Hz$,$ Y$-$connected, three$-$phase squirrel cage induction motor has the following parameters, in $/$phase referred to the stator: R$1=0\mathrm{.}220,$ X$1=0\mathrm{.}430,$ Xm $=15\mathrm{.}0,$ R$2=0\mathrm{.}127$ and X$2=0\mathrm{.}430.$ Its rated slip is equal to $0\mathrm{.}04.$ Mechanical and core losses can be neglected. Compute: A$)$ The torque at rated speed; B$)$ The power factor at rated speed; C$)$ The shaft speed when the load torque is reduced to half rated torque; D$)$ Now consider that the motor is supplied with a frequency converter. What should be the frequency supplied by the frequency converter to the motor so that it operates with half rated speed and rated slip $($s $=0\mathrm{.}04)?$