Problem $3\mathrm{.}63!$

A fuel pump is driven by a motor$-$powered flywheel. The pump behaves as a spring with stiffness $2\frac{N}{m}m$ that is unstretched when $=+-60.$ Neglect any possible dynamic effects.

$($a$)$ Determine the largest tensile and compressive forces spring $AB$ experiences during one revolution of the flywheel, and state the positions $$ where these occur.

$($b$)$ Without further analysis, is it certain that the largest tensile and compressive forces in crank arm $BC$ occur at the same positions $$ determined in Part $($a$)?$ Explain.