Hi..i need to determine the inverse laplace of F(s)=((s^2)-(∏^2))/((s^2)+(∏^2))^2..........by either differentiation or integration of Transforms method..no other methods..i know thee inverse laplace of this s-domain function is t cos(∏t) but i cant figure out a way to show this through either of the two methods mentioned.plz help thanks
its F(s)=((s^2)-(∏^2)) / ((s^2)+(∏^2))^2....the denominator is squared not the whole expression and i am supposed to determine the inverse laplace through either differentiation or integration of laplace.i.e by either using......L{tf(t)}= -F'(s)...or......L{f(t)/t}=∫F(s).ds(the limit is from 0 to ∞)
Squaring just the denominator, then: You do the next part, and indicate where you get stuck. There are common identities available in your textbooks for the solutions, if you want to check. If you could reply in either LaTeX like I have or some other way that makes it easy to read, you would increase the chances of getting a reply.
To use any one of the methods mentioned i have to either first differentiate it or integrate it with respect to s and then take their inverse laplace and then multiply or divide by t depending upon whether i am following differentiation method or integration..thats the approach i am supposed to follow. you are just telling me to get the answer out straight foreward by taking inverse laplace.
if i differentiate i get this.now the inverse laplace of this is equal to -tf(t)...now how can i show that f(t)=tcos(pi.t)?