karoeiu/4_raplace_7.md Secret

Created September 11, 2021 02:29

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4_raplace_7.md

$\begin{align*} \mathcal{L}[e^{\alpha t} \cos(\omega t)] &= \frac{s-\alpha}{(s-\alpha)^{2} + \omega^{2}} \\ \mathcal{L}[e^{\alpha t} \sin(\omega t)] &= \frac{\omega}{(s-\alpha)^{2} + \omega^{2}} \\ \mathcal{L}[t \cos(\omega t)] &= \frac{s^{2} - \omega^{2}}{(s^{2} + \omega^{2})^{2}} \\ \mathcal{L}[t \sin(\omega t)] &= \frac{2\omega s}{(s^{2} + \omega^{2})^{2}} \end{align*}$

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