1. The problem statement, all variables and given/known data Find the laplace transform of t sin(t) and t cos(t), and the inverse transform of 2. The attempt at a solution I found the two laplace forms: and I guess I'm supposed to use the two laplace transforms to find the inverse of this one, but I don't know how to do that.
hi, 1/(1+s²)² can be written as 1/2[(s²+1-(s²-1))/(s²+1)²] this can be split as 1/2[(s²+1)/(s²+1)²] - 1/2[(s²-1)/(s²+1)²] 1/2{[1/(s²+1)] - [(s²-1)/(s²+1)²]} inverse of 1/(s²+1) is sin t and the inverese of next term is (t cost). Just to bring the denominator in appropriate form we have rearranged as in 1st step.
just splitting (a - b)/c as a/c - b/c where a=s²+1 , b = s² - 1 and c= (s² + 1)². is this the step you were referring to?