How can we take the inverse Laplace transform of f_1(s)X(s)+f_2(s)(e^(i phi)X(s−i alpha_1)+e^(-i phi) X(s+i alpha_1))=f_0(s)

Tia English 2022-10-01 Answered
How can we take the inverse Laplace transform of
f 1 ( s ) X ( s ) + f 2 ( s ) ( e i ϕ X ( s i α 1 ) + e i ϕ X ( s + i α 1 ) ) = f 0 ( s )
Where f 1 ( s ) is in the form of f 2 ( s ) f 3 ( s ) , f 2 ( s ) = k 0 s, and f 0 ( s ) is in the form of k 1 + f 4 ( s ) s ( s 2 + α 0 2 ) f 2 ( s )
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Answers (1)

Farbwolkenw
Answered 2022-10-02 Author has 6 answers
Hint.
Anti-transforming
e i ϕ X ( s i α 1 ) + e i ϕ X ( s + i α 1 ) = G 0 ( s ) + G 1 ( s ) X ( s )
we get at
cos ( α 1 t + ϕ ) x 3 ( t ) = 0 t g 1 ( τ ) x 3 ( t τ ) d τ + g 0 ( t )
an integral equation for x 3 ( t )
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