Laplace Transform: Get the Answers You Need

kukumaluboy
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Gimme CLue
 
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kukumaluboy said:
Gimme CLue

You can stick that function directly into the integral formula which defines the inverse Laplace transform and try to calculate it out.

You can use a Laplace transform table. This approach starts by doing a partial fraction expansion of your function. Then the resulting sum of terms can be inverse transformed by matching with transforms in a table. Remember that a Laplace transform is a linear operator.
 
Here's a big hint. What do you get if you differentiate the following with respect to s:

\frac s {s^2+4}
 
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Investigate factoring/expanding some terms, and see what you get. In the end, I do not even think you are going to have to use a partial fraction decomposition to do the problem. The terms in the fraction are chosen with reason in this problem, i.e. it is much simpler than is written.

What have you attempted?
 
Ok Solved! LawlQuals you were rite. I did not use partial fractions. Just simplify and the formulae can be used.
 
LawlQuals said:
Investigate factoring/expanding some terms, and see what you get. In the end, I do not even think you are going to have to use a partial fraction decomposition to do the problem. The terms in the fraction are chosen with reason in this problem, i.e. it is much simpler than is written.

What have you attempted?

I thought he asked for a clue, not a solution. :frown:
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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