Let $f=A\sin{\omega t}=x_1$ and $\dot{f}=-A\omega\cos{\omega t}=\dot{x}_1=x_2$. Let the output be $y=cA\omega$, where $c=1$ is a constant. I want to represent this in a state space formulation:

$\dot{x}=Ax+Bu$

$y=Cx+Du$

What will $C$ be? I tried: $A\omega=\frac{A}{t}\arcsin{\frac{x_1}{A}}$, but does this make sense? Another possibility is $A\omega=\frac{-x_2}{\cos{\omega t}}$. Which one should I choose?

Let $f=A\sin{\omega t}=x_1$ and $\dot{f}=A\omega\cos{\omega t}=\dot{x}_1=x_2$. Let the output be $y=cA\omega$, where $c=1$ is a constant. I want to represent this in a state space formulation:

$\dot{x}=\underline{A}x+\underline{B}u$

$y=\underline{C}x+\underline{D}u$

What will $C$ be? I tried: $A\omega=\frac{A}{t}\arcsin{\frac{x_1}{A}}$, but does this make sense? Another possibility is $A\omega=\frac{-x_2}{\cos{\omega t}}$. Which one should I choose?