Transtormada de Laplace

Tabla de transformadas de Laplace
\( f(t) \)	\( F(s)=\int_0^{\infty}f(t) e^{-st}dt \)
\(\delta(t)\)	1
\(1(t)\)	\(\displaystyle\frac{1}{s}\)
\(t \)	\(\displaystyle\frac{1}{s^2}\)
\(e^{-at} \)	\(\displaystyle\frac{1}{s+a}\)
\(\sin \omega t\)	\(\displaystyle\frac{\omega}{s^2+\omega^2}\)
\(\cos \omega t\)	\(\displaystyle\frac{s}{s^2+\omega^2}\)
\( e^{-\alpha t}\sin\omega t\)	\(\displaystyle\frac{\omega}{(s+\alpha)^2+\omega^2}\)
\( e^{-\alpha t}\cos\omega t\)	\(\displaystyle\frac{s+\alpha}{(s+\alpha)^2+\omega^2}\)