Answer to Question #236292 in Chemical Engineering for Lucky

Question

1)Find the Laplace transform of sinh t/t?

Explain the problem with step by step process?

Answer 1

e^(at) sin(t)= im e( at+it). Laplace transform will be

= 1/(s-(at+i1) = (s-a+i 1)/( (s-a)^2 +1). Imaginary part is 1/(s-a)^2 +1). Now take derivative wrt

a.

L( t e^(at) sin t) = 1/((s-a)^2+1))^2.

Put a=1. You get Laplace transform of t e^t sin t= 1/((s-1)^2+1)^2