A mass of \(20 \mathrm{~kg}\) is suspended from a spring of stiffness \(10,000 \mathrm{~N} / \mathrm{m}\). The vertical motion of the mass is subject to Coulomb friction of magnitude \(50 \mathrm{~N}\). If the spring is initially displaced downward by \(5 \mathrm{~cm}\) from its static equilibrium position, determine

(a) the number of half cycles elapsed before the mass comes to rest,

(b) the time elapsed before the mass comes to rest, and

(c) the final extension of the spring.