Obtain Laplace transforms for the function sin(t-pi) step (t−pi)

Tobias Ali 2021-09-24 Answered
Obtain Laplace transforms for the function \(\displaystyle{\sin{{\left({t}−π\right)}}}\) step \(\displaystyle{\left({t}−π\right)}\)

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Expert Answer

comentezq
Answered 2021-09-25 Author has 10206 answers
Using the delay theorem, we know that \(\displaystyle{L}{\left\lbrace{g{{\left({t}\right)}}}{s}{t}{e}{p}{\left({t}-{c}\right)}\right\rbrace}={c}^{{-{c}{s}}}{L}{\left\lbrace{g{{\left({t}+{c}\right)}}}\right\rbrace}\)
Thus:
\(\displaystyle{L}{\left\lbrace{\sin{{\left({t}-\pi\right)}}}{s}{t}{e}{p}{\left({t}-\pi\right)}\right\rbrace}={e}^{{-\pi{s}}}{L}{\left\lbrace{\sin{{\left({t}+\pi-\pi\right)}}}\right\rbrace}={e}^{{-\pi{s}}}{L}{\left\lbrace{\sin{{t}}}\right\rbrace}={e}^{{-\pi{s}}}\frac{{1}}{{{s}^{{2}}+{1}}}=\frac{{{c}^{{-\pi{s}}}}}{{{s}^{{2}}+{1}}}\)
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