Problem $5.(8$ points$)$

Following nonlinear system with a nonlinear term $f(x)$ is shown below where $f(x)=\frac{si{n}^2(x(t))}{x(t)}$

$x^{\text{'}\text{'}}(t)=-x^{\text{'}}(t)+f(x)$

$(5$ points$)$ Linearize the nonlinear part of the system around the origin $(0,0)$ point. Hint: Use the Linearization technique

$(3$ points$)$ After linearization, show the final linear system in state$-$space form