The Attempt at a Solution
Below is a screenshot of my Maple worksheet. I am currently stuck on part (a). I have taken the Laplace transform of both sides of the equation, solved for Z(s), then converted it Heaviside form, yet Maple cannot compute the inverse transformation! So, I've done something wrong, but I cannot figure out what! Could I have a few pointers please? (bear in mind this is coursework, so it's really only appropriate that you guide me in the right direction rather than explicitly giving any steps towards the solution)
Note that there's something funny with the rendering of the sum notation. In the middle of the "∑" you'll see a "K" - this should be above the ∑ symbol because the sum is from k = 0..K.
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