Perform the inverse Laplace transforms for the following functions: (i) F(s) = (ii) F(S) =49 (F(s)=+-+?...

 

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Perform the inverse Laplace transforms for the following functions: (i) F(s) = (ii) F(S) =²49 (F(s)=+-+? (L1) a, f (t) + a₂ f₂ (t)+...+ a f(t) (L2) f(ct) (L3) 1 (LA) t (L5) teat (L6) t" (ne {0,1,2,...}) (L7) h(t-to) f(t-to) = { (18) eªt f(t) (19) f'(t) (L10) f"(t) (L11) (412) f(") (t) (n={1,2,3,...}) 0 f(t)dr (L13) et (L14) et - eb (L15) sin(@t) (L16) cos(@t) f(t-to), t2to 0, t< to (L17) et sin (@ot) (L18) at cos( t) (L19) 8 (t) ("Dirac delta function") a₁ F (s) + a₂ F₂ (s) +...+ a, F (s) 1 S 1 s² 1 (s-a)² n! s+1 e-os F(s) F(s-a) SF (s)-f(0) s² F(s)- sf (0)- f' (0) s" F(s) - F(s) S 1 s-a a-b (s-a) (s-b) (0) s² +0 S s² +0 k=1 S-k f(k-1) (0) (0) (s+ a)² + 0 ² 1 s+ a (s+a)² + ² Perform the inverse Laplace transforms for the following functions: (i) F(s) = (ii) F(S) =²49 (F(s)=+-+? (L1) a, f (t) + a₂ f₂ (t)+...+ a f(t) (L2) f(ct) (L3) 1 (LA) t (L5) teat (L6) t" (ne {0,1,2,...}) (L7) h(t-to) f(t-to) = { (18) eªt f(t) (19) f'(t) (L10) f"(t) (L11) (412) f(") (t) (n={1,2,3,...}) 0 f(t)dr (L13) et (L14) et - eb (L15) sin(@t) (L16) cos(@t) f(t-to), t2to 0, t< to (L17) et sin (@ot) (L18) at cos( t) (L19) 8 (t) ("Dirac delta function") a₁ F (s) + a₂ F₂ (s) +...+ a, F (s) 1 S 1 s² 1 (s-a)² n! s+1 e-os F(s) F(s-a) SF (s)-f(0) s² F(s)- sf (0)- f' (0) s" F(s) - F(s) S 1 s-a a-b (s-a) (s-b) (0) s² +0 S s² +0 k=1 S-k f(k-1) (0) (0) (s+ a)² + 0 ² 1 s+ a (s+a)² + ²