Laplace transform of \(\displaystyle{f{{\left({t}\right)}}}={t}{e}^{{-{t}}}{\sin{{\left({2}{t}\right)}}}\)

Zane Decker 2022-04-14 Answered
Laplace transform of f(t)=tetsin(2t)
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Answers (2)

maggionmoo
Answered 2022-04-15 Author has 16 answers
Here is an approach.
L(sin2t)=2s2+22=2s2+4 , using the table.
L(etsin2t)=2(s+1)2+4 , using frequency shifting.
L(tetsin2t)=dds(2(s+1)2+4)=4(s+1)((s+1)2+4)2 , using frequency differentiation.
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veselrompoikm
Answered 2022-04-16 Author has 12 answers
Let f(t)=tetsin(2t)=tg(t) and g(t)=etsin(2t)=eth(t) with h(t)=sin(2t). So F(s)=G(s) and G(s)=H(s+1) with H(s)=2s2+4
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