• Find the Laplace transform of the following function when t is the main variable (A and w are constants). f(t) = A cos

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Find The Laplace Transform Of The Following Function When T Is The Main Variable A And W Are Constants F T A Cos 1 (68.66 KiB) Viewed 31 times

• Find the Laplace transform of the following function when t is the main variable (A and w are constants). f(t) = A cos(wt + p)u(t) • Solution: = £ / (+₁ j(wt+p) +e-i(wt+d))u(t)] A = = 4 (ejº L[elwtu(t)] + e¯jº L[e−jwtu(t)] e-atu(t) F(s) = L = A ejø e-jø + -jw s + jw 。jø + e-jø 2 = jo -)s s² +w² cos 0 = ⇒ F(S) = A eje Euler's Identity: Euler's Identity eje = cos 0 + j sin 0 + e-jo 2 A (ei (s+jw) + e¯j (s — jw)) 2 s² +w² 1 s+a (cos)s (sin p)w s² +w² sin 8 = eje - e-je 2j Page 8