Question $1$:

$[5$ Marks$]$

A rotor has the following properties.

$\backslash$table$[[$Mass$,$magnitude,Radius,Angle,$\backslash$table$[[$Axial distance$],[$from first mass$]]],[1,8$ kg$,100$ mm$,{}_A=0,-],[2,7$ kg$,120$ mm$,{}_B=75,125$ mm$],[3,9$ kg$,140$ mm$,{}_C=120,410$ mm$],[4,6$ kg$,120$ mm$,{}_D=310,525$ mm$]]$

If the shaft is balanced by two counter masses located at $100$ mm radii and $120$ mm respectively and revolving in planes midway of planes $1$ and $2,$ and on a distance of $80$ mm on the right of plane $4,$ find the followings:

$($a$)$ Draw two space diagrams: $($i$)$ the positions of the planes along the shaft and $($ii$)$ the angular positions of the masses $($angles measured from positive x $-$ axis$).$

$[1/2]$

$($b$)$ Construct a table and tabulate all necessary data.

$[1]$

$($c$)$ Choose appropriate scales for the couple and force diagrams and write them clearly.

$[1/2]$

$($d$)$ Draw the couple diagram.

$[1]$

$($e$)$ Draw the force diagram.

$[1]$

$($f$)$ Determine the magnitude of the balance masses.

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$($g$)$ Determine the angular positions of the balance masses from the positive $x-$ axis.

$[1/2]$