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Consider the function $f(t)$ having Laplace transform $$F(s)=\frac{\omega_0}{s^2+\omega_0^2} \operatorname{Re}[s]>0$$ The final value of $f(t)$ would be

1. $0$
2. $1$
3. $-1 \leq f(\infty) \leq 1$
4. $\infty$