The spring AB with constant $k$ is undeformed when $=0.$ Given that $R=10in,$

$a=20in,$ and $k=5l\frac{b}{i}n,$ you are asked to:

A$.$ Determine the weight W corresponding to the equilibrium position as a

function of $.$

B$.$ Plot the relation between W and $,$ where W is the weight that maintains the

system in equilibrium, and $$ varies from $0$ to $90.$

C$.$ Determine the value of $$ that minimizes the weight W required to maintain

equilibrium, considering that $$ varies from $0$ to $90.$