LT - { a, } f ′′ ( t ), with f ′ ( t ) continuous and...

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Laplace Transform Table (Adapted from Table 5.1 of Kohler and Johnson) Time Domain Function f ( t ) , t 0 Laplace Transform F ( s ) a a s s > 0 h ( t ) = b 1 , t 0 0 , t < 0 1 s s > 0 t n , n = 1 , 2 , 3 ... n ! s n +1 , s > 0 e αt 1 s - α , s > α sin( ωt ) ω s 2 + ω 2 , s > 0 cos( ωt ) s s 2 + ω 2 , s > 0 sinh( αt ) α s 2 - α 2 , s > | α | cosh( αt ) s s 2 - α 2 , s > | α | e αt f ( t ), with | f ( t ) | ≤ Me at F ( s - α ) , s > α + a e αt h ( t ) 1 s - α , s > α e αt t n , n = 1 , 2 , 3 ... n ! ( s - α ) n +1 , s > α e αt sin( ωt ) ω ( s - α ) 2 + ω 2 , s > α e αt cos( ωt ) ( s - α ) ( s - α ) 2 + ω 2 , s > α
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Time Domain Function f ( t ) , t 0 Laplace Transform F ( s ) f ( t - α ) h ( t - α ) , α 0 with | f ( t ) | ≤ Me at e αs F ( s ) , s > a h ( t - α ) , α 0 e αs s , s > 0 f ( t ), with f ( t ) continuous and | f ( t ) | ≤ Me at sF ( s ) - f (0) , s > max
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Unformatted text preview: { a, } f ′′ ( t ), with f ′ ( t ) continuous and | f ′′ ( t ) | ≤ Me at s 2 F ( s )-sf (0)-f ′ (0) , s &gt; max { a, } i t f ( u ) du , with | f ( t ) | ≤ Me at F ( s ) s , s &gt; max { a, } 1 2 ω 3 (sin ωt-ωt cos ωt ) 1 ( s 2 + ω 2 ) 2 , s &gt; t 2 ω sin ωt s ( s 2 + ω 2 ) 2 , s &gt; tf ( t )-F ′ ( s )...
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LT - { a, } f ′′ ( t ), with f ′ ( t ) continuous and...

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