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.

\(\frac{1}{2} \ddot{x}+\dot{x}+3 x|x|=\frac{1}{3}+\cos t, \quad x(0)=-\frac{1}{2}, \quad \dot{x}(0)=0\)