The Laplace transform of u(t - 2) is a) 1/s + 2 b) 1/s - 2

Lipossig 2021-09-24 Answered
The Laplace transform of \(\displaystyle{u}{\left({t}-{2}\right)}\) is
(a) \(\displaystyle\frac{{1}}{{s}}+{2}\)
(b) \(\displaystyle\frac{{1}}{{s}}-{2}\)
(c) \(\displaystyle{e}^{{2}}\frac{{s}}{{s}}{\left({d}\right)}\frac{{e}^{{−{2}{s}}}}{{s}}\)

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Expert Answer

Bentley Leach
Answered 2021-09-25 Author has 16954 answers
We know that:
\(\displaystyle{L}{\left({u}{\left({t}\right)}\right)}=\frac{{1}}{{s}}\)
By t shifting theorem
\(\displaystyle{L}{\left({u}{\left({t}-{2}\right)}\right)}={e}^{{-{2}{s}}}{L}{\left({u}{\left({t}\right)}\right)}=\frac{{{e}^{{-{2}{s}}}}}{{s}}\)
Answer would be
\(\displaystyle{\left({d}\right)}\frac{{{e}^{{-{2}{s}}}}}{{s}}\)
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