## Laplace & Inverse Laplace Transforms

1. The problem statement, all variables and given/known data
L[f(t)]= 1/(s^2+1)^2 + 1/(s^2+1)
L[f(t)]= ln(s+a) where 'a' is a constant

2. Relevant equations

3. The attempt at a solution
I know that the inverse laplace of 1/(s^2+1) is sin(t), but how do I deal with the squared form of it.

I have never encountered a logarithmic funcion for laplace, so can it be inverted back to f(t) with some of the common solution of conversion?

Thanks
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Mentor
 Quote by 2RIP 1. The problem statement, all variables and given/known data L[f(t)]= 1/(s^2+1)^2 + 1/(s^2+1) L[f(t)]= ln(s+a) where 'a' is a constant 2. Relevant equations 3. The attempt at a solution I know that the inverse laplace of 1/(s^2+1) is sin(t), but how do I deal with the squared form of it. I have never encountered a logarithmic funcion for laplace, so can it be inverted back to f(t) with some of the common solution of conversion? Thanks
For the first problem, and using a table of Laplace transforms, I see that:
L(1/(2w^2)(sin (wt) - wt cos(wt)) = 1/(s^2 + w^2)^2
and L(sin(wt)) = w/(s^2 + w^2)

I'm stumped on the other problem
 Recognitions: Gold Member Science Advisor Staff Emeritus No elementary function has ln(s+a) as its Laplace transform.

## Laplace & Inverse Laplace Transforms

f(t) = (-t)^n[f(t)]
F(s) = F(s)^nth derivative

I believe that's what I got to do for the second one. thanks