The dynamic model of a pendulum is given by \(\frac {d^2θ}{dt^2} + 400 θ = 100 T\), where θ is the displacement in rad / s and T is the applied torque in N-m. Its representation in time scale state variable form Ẋ = α X + βu can have the constants.

• A. \(\alpha = \begin{bmatrix} 0 & 1\\\ -4 & 0\end{bmatrix};\;\beta = \begin{bmatrix} 0 \\\ 1 \end{bmatrix}\)
• B. \(\alpha = \begin{bmatrix} 0 & 1\\\ -4 & 0\end{bmatrix};\;\beta = \begin{bmatrix} 1 \\\ 0 \end{bmatrix}\)
• C. \(\alpha = \begin{bmatrix} 0 & 0\\\ 4 & 1\end{bmatrix};\;\beta = \begin{bmatrix} 0 \\\ 1 \end{bmatrix}\)
• D. \(\alpha = \begin{bmatrix} 0 & 0\\\ -4 & 1\end{bmatrix};\;\beta = \begin{bmatrix} 1 \\\ 0 \end{bmatrix}\)