This had been a question which was bothering me. So here is my question posted on DSP, Stackexchange.

When we were learning Fourier Transforms, we easily derived the fourier transform of **sin(t)** using it's Fourier Series coefficients. But it appeared that the Laplace transform (bilateral) didn't converge. So then I computed the laplace transform for sin(t)*u(t).

*(in other words, computing the Unilateral Laplace Transform of sin(t) )*

How can it happen? Here's the expert answer..

References:

https://math.stackexchange.com/questions/1478497/unilateral-and-bilateral-laplace-transorm