The mathematical model of a nonlinear system is given in the following, where \(u(t)\) is the unit-step input.

a. Plot \(x_{2}(t)\) by simulating the Simulink model.

b. Derive the linearized model analytically, and use the initial command to plot the time variations of the variable that is compatible with \(x_{2}(t)\). Compare the plots generated in (a) and (b) and comment.

c. Find the linear model by using the linearization procedure in Simulink. Plot the response \(x_{2}(t)\) to confirm the result of (b).

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x = X2 x(0) = 0.4 0t10 [x2 = | |x = xx x1 x2+u(t) ' x2(0)=-1