A nonlinear model is given.

a. Obtain the linear state-space form in Simulink.

b. Derive the linearized model analytically to confirm the result of (a).

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