GATE 2023 Electrical Engineering Q46

Question

Consider the state-space description of an LTI system with matrices
A = $\begin{bmatrix} 0 & 1 \ -1 & -2 \end{bmatrix}$, B = $\begin{bmatrix} 0 \ 1 \end{bmatrix}$, C = $\begin{bmatrix} 3 & -2 \end{bmatrix}$, D = 1
For the input, sin($\omega$t), $\omega$ > 0, the value of $\omega$ for which the steady-state output of the system will be zero, is __________. (Round off to the nearest integer).