Problem $4$: For the system shown in Figure $3,$

$($a$)$ Write the second$-$order differential equation which is the equation of motion for each of

the masses $1,2,i,n.$

$($b$)$ Write the equations of motion in state variable form. The end result should be a matrix of

the form $y^{}=Ay$ where $y^{}$ and $y$ are vectors.

Figure $3.$ System for Problem $4.$ Goodwine, $2011.$