A $2-$pole, $208$ V$,60$ Hz three$-$phase induction motor presents the following parameters in a per$-$phase basis: R$1=0\mathrm{.}2,$ X$1=0\mathrm{.}41,$ XM $=15,$ RC $=$ $,$ R$2=0\mathrm{.}12,$ X$2=0\mathrm{.}41.$ The rated slip is $5\%.$ The friction and windage losses amount to $250$ W$.$ Calculate: a$)$ The rated shaft speed; b$)$ The rated power factor; c$)$ The rated shaft power; d$)$ The motor is fed from a frequency converter. It spins at $1800$ rpm with rated slip. Determine the frequency of the voltage supplied to the motor.