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Determine £¯¹{F}. sF(s) - 4F(s) = 4s +5 2 s +8s + 16 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace £¯¹{F} =
Table of Laplace Transforms C t, n=1,2,... 50 f(t) C 1 e att, n=1,2,... at sin bt cos bt at at sin bt cos bt F(s)=L{f}(s) 1 S 1 S S S> 0 s-a n! n+1-s>0 b 2 2 E 2 S + S + b² n! S>0 (s-a)n +1 b S> 0 S> 0 1 (s-a)² + b² s-a 1 (s-a)² + b² spa spa Spa
Properties of Laplace Transforms L{f+g} = £{f} + £{g} L{cf} c{f} for any constant c inn L{e alf(t)} (s) = L{f}(s-a) £{f} (s) = s£{f}(s)-f(0) L {f'') (s) = s² £{f}(s) - sf(0) - f'(0) L {f(")} (s) = s" L{f}(s) - sn-¹f(0) - s^-²f'(0) - ... – f(n − ¹) (0) dn £{t" f(t)} (s) = ( − 1)" -(L{f}(s)) ds {F₁} + £¯¹ (F₂) £¯ {F₁+F₂} = £¯ ¹ (F £¹{cF} = c£¯ {F}