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Laplace transform of $$e^{\theta t} \sin(\omega t)$$ is:
$$\frac{\theta}{S^2 + \omega^2}$$
$$\frac{\omega}{(S - \theta)^2 + \omega^2}$$
$$\frac{S}{S^2 - (\theta - \omega)^2}$$
$$\frac{\omega}{(S + \theta)^2 - \omega^2}$$
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