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.

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