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I'm also struggling to see what the frequency or s-domain actually tells me. Our lecturer gave an example where three sine waves were on top of each other and that it would be difficult to see exactly how many and at what frequencies they were. By doing a Laplace transform we could see the frequency along the s-axis and their amplitude along the y-axis, but what about doing the Laplace transform of a constant? A constant doesn't have a frequency, neither does a function like e^t. The Laplace transform of e^t is 1/s, what kind of information will that function give me? I can set s=2 which will give y=0.5, does it say that the amplitude is 0.5 when the frequency is 2hz? That makes no sense at all :(