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An LTI system having transfer function $\frac{s^{2}+1}{s^{2}+2 s+1}$ and input $x(t)=\sin (t+1)$ is in steady state. The output is sampled at a rate $\omega_{s} \; \mathrm{rad} / \mathrm{s}$ to obtain the final output $\{y(k)\}$. Which of the following is true?

- $y(\cdot)$ is zero for all sampling frequencies $\omega_{s}$
- $y(\cdot)$ is nonzero for all sampling frequencies $\omega_{s}$
- $y(\cdot)$ is nonzero for $\omega_{s}>2$, but zero for $\omega_{s}<2$
- $y(\cdot)$ is zero for $\omega_{s}>2$, but nonzero for $\omega_{s}<2$