The mathematical model of a nonlinear system is provided. Using the procedure outlined in this section, find the operating point and derive the linearized model.

\(\ddot{x}+\frac{2}{3} \dot{x}+f(x)=1+e^{-t / 3}, \quad x(0)=1, \quad \dot{x}(0)=\frac{1}{3}, \quad f(x)=\left\{\begin{array}{lll}3 \sqrt{x} & \text { if } & x \geq 0 \\ -3 \sqrt{|x|} & \text { if } & x \leq 0\end{array}\right.\)