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The following article will add knowledge about “8) Find the inverse Laplace transform F(s) = cot-1 (s – 2)“. Let’s keep an eye on the content below!
Question: 8) Find the inverse Laplace transform F(s) = cot^-1 (s – 2)
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8) Find the inverse Laplace transform
F(s) = cot-1 (s – 2)
Answer
F(s) = cot-1(s-2)
Because we all know this already
f(t) = L-1 [ F(s) ] = ( -1/ t) L-1[F'(s) ]
so we first calculate F'(s) ,
F'(s) = -1 / [(s-2)^2 + 1 ]
Now, put this value
f(t) = (-1/t) L-1[ -1 / [(s-2)^2 + 1 ] ]
= (1/t) L-1[1 / (s-2)^2 + 1]
By using the inverse laplace formula,
(e^at)sinbt = b /(s-a)^2 + b*b
= (1/t )*[(e^2t)sint ]
= (e^2t)sint / t
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