laplacetransform

# laplacetransform - Table 1 Table of Laplace Transforms...

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Table 1: Table of Laplace Transforms Number f ( t ) F ( s ) 1 δ ( t ) 2 u s ( t ) 3 t 4 t n at 5 e 6 te at 1 t n 1 at 7 e ( n 1)! at 81 e 9 e at e bt 10 be bt ae at 11 sin at 12 cos at 13 e at cos bt 14 e at sin bt 15 1 e at (cos bt + a b sin bt ) 1 1 s 1 2 s n ! s n +1 1 ( s + a ) 1 ( s + a ) 2 1 ( s + a ) n a s ( s + a ) b a ( s + a )( s + b ) ( b a ) s ( s + a )( s + b ) a 2 s 2 + a s 2 s 2 + a s + a ( s + a ) 2 + b 2 b ( s + a ) 2 + b 2 a 2 + b 2 s [( s + a ) 2 + b 2 ] 1

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Table 1: Properties of Laplace Transforms Number Time Function Laplace Transform Property 1 αf 1 ( t )+ βf 2 ( t ) αF 1 ( s βF 2 ( s ) Superposition 2 f ( t T ) u s ( t T ) F ( s ) e sT ; T 0 Time delay 3 f ( at ) 1 a F ( s a ); a> 0 Time scaling 4 e at f ( t ) F ( s + a ) Shift in frequency 5 6 df ( t ) dt d 2 f ( t ) dt 2 sF ( s ) f (0 ) s 2 F ( s ) sf (0 ) f (1) (0
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laplacetransform - Table 1 Table of Laplace Transforms...

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