Problem $1$:

A single $-$cylinder reciprocating engine has a reciprocating mass of $60$ kg $.$ The crank

rotates at $60$ rpm and the stroke is $320$ mm $.$ The mass of the revolving parts at $160$ mm

radius is $40$ kg $.$ If two$-$thirds of the reciprocating parts and the whole of the revolving

parts are to be balanced, determine the, $($i$)$ balance mass required at a radius of $350$ mm

and $($ii$)$ unbalanced force when the crank has turned $50^($@$)$ from the top$-$dead centre.

Also show the diagram of graphs.