$\backslash$table$[[$r$1,12,$r$2$P$,13,],[$r $1,$given,$100,$siven,cm$],[$theta $1,$theta $2,$theta $2$ P$,$theta $3,$TIMT$],[$given$,$siven,theta $2,$theta $3,$degrees$]]$

An adjustable exercise bench shown in the picture, schematic and vector model. In this bench, the adjustment holes are on the rear bench leg $($r$1).$ You need to determine the velocity of the bench components based on the rate at which the back of the bench is rotated $($omega$\_2).$ All Units are $cm,c\frac{m}{s},$ radians, radians$/$s

Solve for angular velocity of link $3($omega $3)$ based on input omega $2.$ Use the method covered in class.

Assume that the angular velocity of the bench $($omega $2)$ is given.

Given data is here and on figure and table, $r1=122$; theta$1=2\mathrm{.}7053$;$r2=75$; theta $2=0\mathrm{.}5236$; omega $2=1\mathrm{.}7$;$r3=101$; theta $3=2\mathrm{.}0769$;$r2P=100$;

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