Two stepper motors are used in an open loop system to drive the leadscrews for x$-$ypositioning. The range of each axis is $550$ mm$.$ The shafts of the motors are connected directly to the leadscrews $($no gear reduction$).$ The leadscrew pitch is $5\mathrm{.}0$ mm$,$ and the number of step angles on each motor is $120.($a$)$ How closely can the position of the table be controlled, assuming there are no mechanical errors in the positioning system? $($b$)$ What are the required rotational speeds of each stepper motor and corresponding pulse train frequencies to drive the table at $300$ mm$/$min in a straight line from point $($x $=0,$ y $=0)$ to point $($x $=330$ mm$,$ y $=220$ mm$)?$