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TRANSFORMADA DELAPLASE

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  • Tabla de Transformadas de Laplace

    L {f (t)} = 0 es t f (t) dtf(t) F (s) f(t) F (s)

    1. 11

    s2. tn, n = 1, 2, 3, ..

    n!

    sn+1

    3. t, 1 < (+ 1)s+1

    4. ea t1

    s a

    5. tn ea t, n = 1, 2, 3, ..n!

    (s a)n+1 6. sin ( t)

    s2 + 2

    7. cos ( t)s

    s2 + 28. sinh ( t)

    s2 2

    9. cosh ( t)s

    s2 2 10. ea t sin ( t)

    (s a)2 + 2

    11. ea t cos ( t)s a

    (s a)2 + 2 12. t sin ( t)2 s

    (s2 + 2)2

    13. t cos ( t)s2 2

    (s2 + 2)214. sin ( t) t cos ( t) 2

    3

    (s2 + 2)2

    15. sin ( t) + t cos ( t)2 s2

    (s2 + 2)216.

    1

    a b(ea t eb t

    ) 1(s a) (s b)

    17.1

    a b(a ea t b eb t

    ) s(s a) (s b) 18.

    1

    a2(1 cos (a t)) 1

    s (s2 + a2)

    19.1

    a3(a t sin (a t)) 1

    s2 (s2 + a2)20. f(t) + g(t) F (s) +G(s)

    21. c f(t) c F (s) 22. f (t) s F (s) f(0)

    23. f (t) s2 F (s) s f(0) f (0) 24. f (n)(t) sn F (s) sn1 f(0) f (n1)(0)

    25. ea t f(t) F (s a) 26. tn f(t) (1)n dn

    dsnF (s)

    27. Ua(t) = U(t a) ea s

    s28. f(t a)Ua(t) ea s F (s)

    29. f g = t0

    f(t )g()d F (s)G(s) 30. (t c) ec s

    31. f(t+ T ) = f(t)

    T0

    es t f(t) dt

    1 es T 32. t0

    f() d1

    sF (s)

    33.f(t)

    t

    +s

    F () d 34. f(a t)1

    aF(s

    a

    )

    lims+ s F (s) = f(0) lims0+

    s F (s) = limt+ f(t)

    1

    MATEMTICA IV-INGENIERA CIVIL UNIVERSIDAD ULADECH CATLICA