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Inverse Laplace transform of $$\frac{S}{S^2 + a^2}$$ is
$$\frac{e^{at} + e^{-at}}{2}$$
$$\frac{e^{at} - e^{-at}}{2}$$
$$\frac{e^{at}}{2}$$
$$\frac{e^{-at}}{2}$$
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