Q$6)$ In figure below, the spring is unstretched when $a=0$ and $k$ is the spring constant. Write a MATLAB

program to compute and plot the mass $m$ corresponding to equilibrium as a function of a for values of a

from $0$ to $90.$ Find the value of a corresponding to equilibrium $m=2\mathrm{.}5kg.$ Given $R=210mm,d=50mm$

and $k=1\mathrm{.}2k\frac{N}{m}.$

NOTE : the following equations and figure may be referred

$A{B}_x=d-$Rcos$$

$A{B}_y=$Rsin$$

$AB=\sqrt[\phantom{2}]{A{B}_x^2+A{B}_y^2}$

The tension in the spring is

$T=k[AB-(d-R)]$

The vertical component $T_y$

$T_y=T\frac{A{B}_y}{AB}$

Summing moments about point $C$ gives

$M_C=0$;

$T_{y}d-mgR=0$;$,m=T_y\frac{d}{Rg}$