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TRANSFORMADAS DE LAPLACE f(t) ( ) s F 1. δ(t) (impulso unitário) 1 2. δ A (t) (pulso) ( ) s w t e 1 s h 3. S(t) (degrau unitário) s 1 4. t (rampa) 2 s 1 5. 1 n t ( ) n s ! 1 n 6. bt e b s 1 + 7. τ τ t e 1 1 s 1 + τ 8. ( ) ( ) 0 n ! 1 n e t bt 1 n > ( ) n b s 1 + 9. ( ) τ τ t 1 n n e t ! 1 n 1 ( ) n 1 s 1 + τ 10. ( ) t 1 b t 2 b 2 1 e e b b 1 ( )( ) 2 1 b s b s 1 + + 11. ( ) 2 t 1 t 2 1 e e 1 τ τ τ τ ( )( ) 1 s 1 s 1 2 1 + τ + τ 12. t 2 b 2 1 2 3 t 1 b 1 2 1 3 e b b b b e b b b b + ( )( ) 2 1 3 b s b s b s + + + 13. 2 t 1 2 3 2 2 1 t 2 1 3 1 1 e 1 e 1 τ τ τ τ τ τ τ + τ τ τ τ τ ( )( ) 1 s 1 s 1 s 2 1 3 + τ + τ + τ 14. τ t e 1 ( ) 1 s s 1 + τ 15. t sen ω 2 2 s ω + ω 16. t cos ω 2 2 s s ω + 17. ( ) φ + ωt sen 2 2 s sen s cos ω + φ + φ ω 18. t sen e bt ω b, ω reais ( ) 2 2 b s ω + + ω 19. t cos e bt ω b, ω reais ( ) 2 2 b s b s ω + + +

Transformadas de Laplace

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  • TRANSFORMADAS DE LAPLACE f(t) ( )sF 1. (t) (impulso unitrio) 1 2. A(t) (pulso) ( )swte1sh 3. S(t) (degrau unitrio)

    s1

    4. t (rampa) 2s1

    5. 1nt ( )ns!1n

    6. bte bs

    1+

    7. te1

    1s1+

    8. ( ) ( )0n !1net bt1n >

    ( )nbs1+

    9. ( )

    t1n

    n et!1n1 ( )n1s

    1+

    10. ( )t1bt2b21

    ee bb

    1 ( )( )21 bsbs1

    ++

    11. ( )2t1t21

    ee1 ( )( )1s1s1

    21 ++

    12. t2b21

    23t1b

    12

    13 e bbbb

    e bbbb

    +

    ( )( )21

    3bsbs

    bs++

    +

    13. 2t12

    32

    2

    1t

    21

    31

    1e1e1

    +

    ( )( )1s1s

    1s

    21

    3++

    +

    14. te1 ( )1ss1+

    15. t sen 22s +

    16. t cos 22ss+

    17. ( )+t sen 22ssen scos

    ++

    18. t sene bt b, reais ( ) 22bs ++

    19. t cose bt b, reais ( ) 22bsbs++

    +

  • 20. ( ) ( )10t1sene11 2t

    2