Tabla de transformadas de Laplace

Proporcionamos una tabla de transformadas de Laplace de algunas funciones.

$1.\quad \; f(t)=1 \Rightarrow F(s)= \dfrac{1}{s}.$

$2.\quad \; f(t)=e^{at} \Rightarrow F(s)= \dfrac{1}{s-a}.$

$3.\quad \; f(t)=\operatorname{sen}bt \Rightarrow F(s)= \dfrac{b}{s^2+b^2}.$

$4.\quad\;  f(t)=\cos bt \Rightarrow F(s)= \dfrac{s}{s^2+b^2}.$

$5.\quad \; f(t)=\operatorname{senh}bt \Rightarrow F(s)= \dfrac{b}{s^2-b^2}.$

$6.\quad \; f(t)=\operatorname{cosh}bt \Rightarrow F(s)= \dfrac{s}{s^2-b^2}.$

$7.\quad \; f(t)=t^n\;(n=1,2,\ldots) \Rightarrow F(s)= \dfrac{n!}{s^{n+1}}.$

$8.\quad\; f(t)=t^ne^{at}\;(n=1,2,\ldots) \Rightarrow F(s)= \dfrac{n!}{(s-a)^{n+1}}.$

$9.\quad \;f(t)=t\operatorname{sen}bt \Rightarrow F(s)= \dfrac{2bs}{(s^2+b^2)^2}.$

$10.\quad f(t)=t\operatorname{cos}bt \Rightarrow F(s)= \dfrac{s^2-b^2}{(s^2+b^2)^2}.$

$11.\quad f(t)=e^{-at}\operatorname{sen}bt \Rightarrow F(s)= \dfrac{b}{(s+a)^2+b^2}.$

$12.\quad f(t)=e^{-at}\operatorname{cos}bt \Rightarrow F(s)= \dfrac{s+a}{(s+a)^2+b^2}.$

$13.\quad f(t)=\dfrac{\operatorname{sen}bt-bt\cos bt}{2b^2} \Rightarrow F(s)= \dfrac{1}{(s^2+b^2)^2}.$

$14.\quad f(t)=\dfrac{t\operatorname{sen}bt}{2b} \Rightarrow F(s)= \dfrac{s}{(s^2+b^2)^2}.$