Word Count : 167

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The given function is: \[ F(t) = \begin{cases} \sin\left(t-\frac{\pi}{4}\right), & t > \frac{\pi}{4} \\ 0, & t < \frac{\pi}{4} \end{cases} \] To find the Laplace Transform \( L\{F(t)\} = \mathcal{L}[F(t)] \), we use the Heaviside step function \( u_c(t) \), which ______ ________ ______ _______ ___ ________ ___ _______ ________ _________.
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