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2022-10-17

What is the laplace transform of $\delta \left(t-\pi /6\right)\mathrm{sin}\left(t\right)$

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Marlene Welch

Expert

The Laplace transform is by definition
${\int }_{0}^{\mathrm{\infty }}\mathrm{exp}\left(-st\right)\delta \left(t-\pi /6\right)\mathrm{sin}\left(t\right)dt=\mathrm{sin}\left(\frac{\pi }{6}\right)\mathrm{exp}\left(-s\frac{\pi }{6}\right)=\left(1/2\right)\mathrm{exp}\left(-s\frac{\pi }{6}\right)$

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