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 \(\frac{1}{(1+s^2)^2}\)

2. The attempt at a solution

I found the two laplace forms:

\(\frac{2s}{(s^2+1)^2}\)

and

\(\frac{s^2-1}{(s^2+1)^2}\)

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.

 

hi,
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]

Did you obtain that using separation of variables?

 

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?

 

Then I'm done with maths for this year. Thanks for helping me with all my problems!