Write a MATLAB program that has a main code named HW$4$p$2\_$Task$2\_$UCusername.m and two functions Displacement$\_$UCusername.m and Velocity$\_$UCusername.m$.$

$$ The main code will prompt the user to enter:

o The compressor$$s dimensions L$1,$ L$2,$ and L$3$ in inch

o The initial crank angle $($theta$2)$ in degrees

The rotational speed of the crank $(w_2)$ in RPM

The main code will convert $(w_2)$ to $ra\frac{d}{sec}.$

The main code will create ${}_2$ array that starts from the angle ${}_{2i},$ increments by $10$ up to

a full rotation $({}_{2i}+360).$

Then, the main code will call the function Displacement$\_$UCusername.m and pass $L_1,L_2,L_3,$ and ${}_2.$

The function Displacement$\_$UCusername.m calculates and returns the arrays ${}_3$ and $L_4$ shown in the equations below.

Then, the main code will call function Velocity$\_$UCusername.m and pass $L_2,L_3,{}_2,{}_3$ and $w_2.$

The function Velocity$\_$UCusername.m calculates and returns the arrays $w_3$ and $v_4$ shown in the equations below.

The main code will find the minimum and maximum of $L_4$

The main code will calculate and output the stroke of the piston $=L_4$max$-L_4$min

The main code will plot $L_4$ versus ${}_2$ on Figure $1$ and $v_4$ versus ${}_2$ on Figure $2.$ Add axis

labels $($with units$),$ and titles for both figures.

Hint: Pay close attention to the units for the angles, make sure you are consistent with the

units, use MATLAB Commands sind$,$ cosd$,$ and asind.

Hint: use command figure$(1)$ before $1^{st}$ plot command to create Figure $1$ and command

figure$(2)$ before the $2^{nd}$ plot command to create Figure $2.$

Closed form equations for a slider$-$crank mechanism $[3]$:

${}_3=si{n}^{-1}(\frac{L_1+L_{2}sin{}_2}{L_3})$

$L_4=L_{2}cos({}_2)+L_{3}cos({}_3)$

${}_3=-{}_2(\frac{L_{2}cos{}_2}{L_{3}cos{}_3})$

$v_4=-{}_2{L}_{2}sin{}_2+{}_3{L}_{3}sin{}_3$