$1.)$ Determine the crankshaft angle, theta, for maximum piston velocity of cylinder $1$ in the following engine. stroke $=2$R $=3\mathrm{.}48$in$,$ l $=5\mathrm{.}7$in $($Chevy $350$ in$^3$ engine$)($Hint: max velocity @ acceleration $=0)($Note: It is not at theta $=90$ degrees since R$/$l does not equal $1)$

$2.)$ a$)$ Determine the imbalance forces $+$ moments for a Mercedes in$-$line $5$ cylinder, even firing, $4-$stroke engine. Cylinder Spacing $=105$mm$,$ Stroke $=92\mathrm{.}4$mm$,$ l$/$r $=3\mathrm{.}5,$ m$\_$r $=0\mathrm{.}68$kg$,$ N $=5100$rpm$,$ Firing Order is $1-2-4-5-3-1$

b$)$ How would you balance this engine?