A nonlinear dynamic system model is derived as

\[\dot{x}+2 x^{3}=u(t), x(0)=0,0 \leq t \leq 3\]

where \(u(t)\) is the unit-step function.

a. Build the Simulink model and use it to plot the response \(x(t)\).

b. Derive the linearized model analytically. Build a Simulink model and use it to plot the time variations of the variable in the linear model that is compatible with \(x(t)\). Compare the plots generated in (a) and(b) and comment.