Hi. We are learning about Laplace transforms at uni and I must say that this is a real pain. I have one questions concerning the concept of Laplace transforms, and also a question concerning a specific transform. The task is to make a Laplace transform of: t*sin(2t). I could do an integration by parts and solve it using the standard definition of the Laplace transform, but I don't think that is the idea. The question says "L[f(t)]=F(s). L[t*f(t)]=-dF(s)/ds". I can't find this anywhere in the book other than above the assignment I'm asked to do so there's no explanation of it, I have no idea of what it means :( I was thinking that it might have to do with that L(f')=s*L(f)-f(0), but to use that, I would have to know the Laplace transform of f'(t), but I don't :( Is there anyone that could give me some help?(adsbygoogle = window.adsbygoogle || []).push({});

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 :(

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# Struggling with Laplace transforms

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