The discussion revolves around the Laplace and inverse Laplace transforms, specifically focusing on the expressions L[f(t)]= 1/(s^2+1)^2 + 1/(s^2+1) and L[f(t)]= ln(s+a), where 'a' is a constant. Participants are exploring how to handle the squared term in the first expression and the logarithmic function in the second.
The discussion is ongoing, with participants sharing their attempts and expressing confusion about specific aspects of the problems. Some guidance has been offered regarding the use of Laplace transform tables, but no consensus has been reached on the best approach to the logarithmic function.
Participants are grappling with the implications of using squared terms and logarithmic functions in Laplace transforms, indicating potential gaps in their understanding or resources available for these specific cases.
For the first problem, and using a table of Laplace transforms, I see that:2RIP said:Homework Statement
L[f(t)]= 1/(s^2+1)^2 + 1/(s^2+1)
L[f(t)]= ln(s+a) where 'a' is a constant
Homework Equations
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