Laplace transform problem with multiple parts

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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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