hmmmm.... as I recall from signal and systems, Laplace transformation doesn't exist on periodical signals like u have there ...
there is Laplace transformation of because with step function u put to zero your signal for all t<0, But with like this one u have (periodical) it doesn't converge
P.S. perhaps only if u use unilateral Laplace transformation (but still I'm spinning a lot even that way) which limits go from (-0) to infinity... but as I said i think there's no point going there because it just start going in circles (at least I do)
Edit : without your "constants" (a) and (b) and using unilateral formula (don't know if you are bounded to use bilateral) u get this :
that's for (region of convergence )
without (a), or should i say a=1 u'll get :
that's for
yes, always u can use table of Laplace transformations, but on the exams i don't think anywhere would someone allow you to use table of Laplace transformations... or that's just me
anyway using unilateral u can get to the solution, but using bilateral u can't
solution should be something like:
with