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I have a final coming up next week (Tuesday) and a sample question for the test is the following.

I was wondering if I have properly set it up for solving with Laplace as I haven't encountered a question with two level changes before and it's confussed me.

First line is the question and the second line is my questionable setup. enter image description here

My understanding is that I'm doing this...

level+(newLevel-oldLevel)U(t-PointOfChange)

Finding good examples of Step & Impulse online has proven to be a greater challenge than I thought it would be.

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    I'm not sure what you mean by levels, but if apply the Laplace transform to the right hand side you just get $$\int_\pi^{2\pi} e^{-st}dt,$$ which can be evaluated explicitly, right?2012-06-16
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    It's a graph of 'something' over time. That 'something' could be voltage level or switch on/off indication. So the level could be 0mV/100mV or 0/1.2012-06-16
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    Do you mean $y''+y=f(t)$ since you gave two initial conditions?2012-12-21

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