Ejercicios Laplace

INGENIERIA EN SISTEMAS COMPUTACIONALES
(Sabatino)

ECUACIONES DIFERENCIALES

“Actividad:
Transformada de Laplace.”

Alumno:Jonathan Pedraza Serrano

Asesor:
Gabriel Trujillo Jiménez

29 de marzo de 2012.

Transformada de Laplace.Lt2-3t+5Lt2=2sLt2-1=2s2-1!s2=2!s3=2s3L3t=3Lt=31sLt1-1=31sL1=31s*1s=31s2=3s2L5=50∞e-stdt=5e-sts∞0=5sLt2-3t+5=2s3-3s2+5s |Le-4t+3e-2tLe-4t=0∞e-ste-4tdt=0∞e-(s+4)tdt=e-(s+4)ts+4∞0=1s+4 , s>-4L3e-2t=30∞e-ste-2tdt=30∞e-s+2tdt=3e-s+2ts+2∞0=31s+2=3s+2 , s>-2 Le-4t+3e-2t=1s+4+3s+2 ,s<-2 |
Lte4t0∞e-st(te4t)dt=0∞te-(s-4)tdt=-e-(s+4)ts-42∞0=1s-42 , s>4 |
Lsen2t+cos2tk=2 , Lsen2t=ks2+k2=2s2+22=2s2+4, s>0k=2 , Lcos2t=ss2+k22=ss2+22=ss2+4 , s>0Lsen2t+cos2t=2s2+4+ss2+4=s+2s2+4 , s>0 |Let-e-t3=Le3t-e-3tLe3t=1s-3 , s>3Le-3t=1s+3 , s>-3Le3t-e-3t=1s-3-1s+3 , s>0 |L12t3+t2-112Lt3=123!s4=62s4=3s4Lt2=2!s3=2s3L1=1sL12t3+t2-1=3s4+2s3-1s |
L2e3t-e-3tL2e3t=21s-3=2s-3 , s>3Le-3t=1s+3 , s>-3L2e3t-e-3t=2s-3-1s+3 , s>0 |Lett=Lett-2=Lett2Let=1s-1 , s>-1Lt2=2sLt2-1=2s2-1!s2=2!s3=2s3Lett2=1s-12s3=2s4-s3 |
Le2tcos2tLe2t=1s-2 , s>-2Lcos2t=ss2+22=ss2+4, s>0Le2tcos2t=1s-2ss2+4=ss3-2s2+4s-8 |
Lcos2tk=1 , Lcos2t=s2+2k2ss2+4k2=s2+2(1)2ss2+4(1)2=s2+2ss2+4=s2+2s3+4s |