Nonlinear springs are classified as hard or soft,

Chapter 13, Problem 13.35

(choose chapter or problem)

Nonlinear springs are classified as hard or soft, depending upon the curvature of their force-deflection curve (see figure). If a delicate instrument having a mass of 5 kg is placed on a spring of length l so that its base is just touching the undeformed spring and then inadvertently released from that position, determine the maximum deflection \(x_{m}\) of the spring and the maximum force \(F_{m}\) exerted by the spring, assuming (a) a linear spring of constant k = 3 kN/m, (b) a hard, nonlinear spring, for which \(F=(3 \ \mathrm{kN} / \mathrm{m})\left(x+160 x^{3}\right)\).