A $3-$cylinder engine is shown below. All cylinders lie in a single transverse plane. The three cylinder centerlines are $120$ degrees apart. The crank of length $0\mathrm{.}06$ m rotates at a constant angular velocity of $100$rad$//$s$($ccw$).$ The length of the three identical connecting rods is $0\mathrm{.}6$ m $.$ The mass centers of the connecting rods are at their midpoints. The crank and the rotational mass of the coupler have been balanced with a mass center at the mainline of rotation. The combined reciprocating mass $($the translating mass of each connecting rod and the piston mass$)$ is $2\mathrm{.}5$ kg $.$ Determine $($i$)$ the shaking force magnitudes when the crank rotates to coincide with the three cylinder centerlines, $($ii$)$ devise a balancing scheme and recalculate the shaking force magnitudes at the same three crank positions as in $($i$),$ and $($iii$)$ comment on the effectiveness of your balancing scheme. $[20]$