Help Needed with Laplace Transforms: Solve Before Tomorrow!

emtilt
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I'm posting these as images because it would be difficult to type. If this isn't allowed, please let me know. I really need help with this before tomorrow, when I have a test. Any help appreciated.

Homework Statement


problem here

The Attempt at a Solution



I completed part 1 (solution here) but I cannot get anywhere with part 2. I tried fsimply calculating the Laplace transforms of the results from part 1 and then manipulating them, but I got nowhere. Any help is appreciated.
 

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Thread 'Finding the nth roots of a complex number'

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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