Laplace transform of sin(t^0.5)

Question

mathmale · Answer

I'll begin with what I do remember, in the hope that that might be helpful to you.  The function sin(t^.5) has the form of a composition:  if f(x) and g(x) are functions, and if domains / ranges are not a concern, then letting g(x) be the input to f(x) creates the composition f(g(x)).  Is there a Laplace transform for such a composition?

I'd suggest you search for "tables of Laplace Transforms" on the 'Net.  some are more comprehensive than others.  Youo just may find inspiration in one such table that will help you find the Laplace Transform of the composite function given you.

hartnn · Answer

nicely explained here https://www.youtube.com/watch?v=ca1LuQZRX6s

hartnn · Answer

multiply the final answer he gave by  exp(-1/4s)
which becomes obvious if you watch the entire video

anonymous · Answer

(0.5*√pi *exp(1/4s))(s^1.5)

anonymous · Answer

My answer is coming..

hartnn · Answer

both the exponents need to be negative...