I was trying to use Wolfram Alpha engine to transform a power function using laplace transform and then inverse using inverse laplace transform.
The function is:
D(t) = a*t^b + c
('t' is the initial variable, 's' is the transform variable and 'a', 'b', and 'c' are constant parameters)
When I transfer it using Laplace Transform, I got this results:
a s^(-b-1) Gamma(b+1)+c/s
However, when I try to inverse the result function using the formula: 1/s^2 as shown below:
1/[s^2*(a s^(-b-1) Gamma(b+1)+c/s)]
The engine doesn't give me any results. as shown in the below image:
I keep clicking on 'Solve' button but with no response.
Can anyone help me in finishing this?
Thanks Sean for replying..
Actually, I am trying to follow another example I found. The example is trying to solve the below equation using laplace transform:
So, he got this:
By using this formula:
he became able to identify this:
And using the inverse laplace transform he got this:
Then he compare it with the original relaxation modulus:
To identify each part of the equation as follows:
So, when I tried to follow the above steps, I couldn't inverse the results from laplace transform after multiplying by 1/s^2.
I appreciate your help and explaination..
What result are you expecting for the Inverse Laplace Transform of 1/[s^2*(a s^(-b-1) Gamma(b+1)+c/s)]?
It doesn't show a result becuase it doesn't find any result.
Are you sure you're not looking for the inverse transform of (1/s^2)(a s^(-b-1) Gamma(b+1)+c/s) instead? Are you looking for the convolution of t and a*t^b + c?