Standard pair: L[sin ωt] = ω/(s²+ω²). First shift theorem: L[e^{−at}f(t)] = F(s+a). Applying the shift to F(s)=ω/(s²+ω²) gives ω/[(s+a)²+ω²], i.e. L[e^{−at}sin ωt]. Answer: exp(−at) sin ωt. (B) confuses sin with sinh (denominator would need (s+a)²−ω² for sinh); (C),(D) wrongly include a factor 't'.
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