For a spring-mass-damper system, satisfying My(t) + by(t) + f(t) = u(t) where y(t) is the displacement, u(t) the external force, b the damper coefficient. f(t) = Ky⁴(t) represents a nonlinear spring.
Define 11 = y, 12 = y, and let u be the input, y the output. Obtain a nonlinear state space model for this system.