A tightly wound helical coil spring is made from an \(1.88-\mathrm{mm}\) diameter bar made from 0.2 percent hardened steel ( \(\left.\mathrm{G}=80 \times 10^{9} \mathrm{~N} / \mathrm{m}^{2}, ho=7600 \mathrm{~kg} / \mathrm{m}^{3}\right)\). The spring has a coil diameter of \(1.6 \mathrm{~cm}\) with 80 active coils. Calculate

(a) the stiffness of the spring,

(b) the static deflection when a \(100 \mathrm{~g}\) particle is hung from the spring, and

(c) the equivalent mass of the spring for a SDOF model.