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Determine the inverse Laplace transform of the function below. 2s +32 2 s + 4s+20 Click here to view the table of Laplace transforms Click here to view the table of properties of Laplace transforms. 2s +32 2 s + 4s + 20 -0
Table of Laplace Transforms K f(t) C 2 t", n=1,2,... 1 at sin bt at 2 cos bt eat, n=1,2,... at sin bt cos bt F(s)=L{f}(s) 1 m S 1 S s-a n! n+1- b ,S 0 s +b 1 S s² + b² S n! s-a (s-a)n +1 b (s-a)2 + b S> 0 S0 SPO S> 0 $1 1 2 (s-a)² + b² Spa Spa spa
Properties of Laplace Transforms L{f+g} = £{f} + £{g} {cf} = c{f} for any constant c L{e alf(t)} (s) = £{f}(s - a) L {f} (s) = 2 L {f} (s) = s£{f}(s) - sf(0) = f'(0) L {f(")} (s) = s"£{f}(s) — s"¯¹f(0) - s^-²f′(0) - ... – f(n − ¹) (0) s£{f} (s)-f(0) d {t" f(t)} (s) = ( − 1)¹-(£{f}(s)) ds £¯ ¹ (F₁+F₂} = £¯ ¹ (F) + £¹ (F₂) ✓F. {F2} £{cF} {cF} = CL {F}