Assignment 4: Problem 8 (1 point) Compute the Laplace transform. Your answer should be a function of the variable $s$: $\mathcal{L}\left\{6 + u_{7/2}(t)e^{-2t}\sin(\pi t)\right\} =$ You may find the following formulas useful: $\cos(bt + \pi) = -\cos(bt)$ $\sin(bt + \pi) = -\sin(bt)$ $\cos\left(bt + \frac{\pi}{2}\right) = -\sin(bt)$ $\sin\left(bt + \frac{\pi}{2}\right) = \cos(bt)$ If you don't get this in 2 tries, you can get a hint.
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We want to compute the Laplace transform $\mathcal{L}\{f(t)\}$. The Laplace transform is a linear operator, so we can write $\mathcal{L}\{f(t)\} = \mathcal{L}\{6\} + \mathcal{L}\{u_{7/2}(t)e^{-2t}\sin(\pi t)\}$ Show more…
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