Q$2.[10$ marks$]$ A rigid shaft supports two disks as shown below. Disk $1$ has a mass of $15$ kg and its center of mass is offset by $0\mathrm{.}003$ m in the direction shown. Disk $2$ has a mass of $12$ kg and an offset of $0\mathrm{.}0025$ m in the direction shown. This shaft is to be balanced using a two$-$plane balancing technique. Balancing masses are to be added at the planes P$1$ and P$2.$ Design the locations of P$1$ and P$2,$ the counterbalances $($mass times eccentricity$)$ to be added to these two planes and their orientations so that the shaft is completely balanced.