Question

Find the Laplace transform of e^atsinbt.

(a) b/((s-a)^2+b^2)

(b) b/((s+a)^2+b^2)

(c) b/((s+a)^2-b^2)

(d) b/((s-a)^2-b^2)

The question was posed to me in an online quiz.

I'm obligated to ask this question of Operational Transforms in chapter Intoduction to the Laplace Transform of Network Theory

Answer 1

Correct answer is (a) b/((s-a)^2+b^2)

Easy explanation: The Laplace transform of sinbt is L(sinbt)=b/(s^2+b^2). So the Laplace transform of e^atsinbt is L(exp(at) sinbt)=b/((s-a)^2+b^2).