L {f ( t ) }=∫0

∞

e− st f ( t )dt=F (s ), t>0

silaintegral converge , entonces latransformadaexiste

La transformada es una transformación lineal:

L {af ( t )+bg ( t ) }=a L {f ( t ) }+b L {g (t)} , a , b constantes .

Convolucion:

f∗g=g∗f=∫0

t

f (u )g ( t−u )du=¿ L−1 {L {f }×L {g }}¿

En un caso particular:

µ (t )=∫0

t 1mω0

e−ξωnt sen ( t−u ) p (u ) du

µ (t )=L {sen (t )∗p(t) }

µ (t )= 1mω0

e−ξωn tL−1

{(L {(sen ( t ))}×L { p ( t ) })}