ejercicios de transformada de laplaceDescripción completa
INFORME TRANSFORMADA TRANSFORMADA DE LAPLACE
LUIS FERNANDO JIMENEZ HERNANDEZ LUIS FERNANDO HERNANDEZ VERONA ANDRES FELIPE MIELES DANIEL VIAFARA
21/05/2016
Transformada de Laplace La Transfr!a"a "# La$%a #s 'na ()&n*&a Ma(#!+(*&a ,'# fr!a $ar(# "# &*#r(as transformadas integrales &! %a (ransfr!a"a "# F'r*#r- %a (ransfr!a"a "# H*%.#r(- %a (ransfr!a"a "# M#%%*n #n(r# (ras Es(as (ransfr!a"as #s(+n "#n*"as $r !#"* "# 'na *n(#ra% *!$r$*a cambian una función en una variable de entrada en otra función en otra variable La (ransfr!a"a "# La$%a $'#"# s#r 'sa"a $ara r#s%3#r E&'a&*n#s D*f#r#n&*a%#s L*n#a%#s E&'a&*n#s In(#ra%#s A'n,'# s# $'#"#n r#s%3#r a%4n (*$ "# ED &n &#&*#n(#s 3ar*a.%#s- #n #n#ra% s# a$%*&a a $r.%#!as &n &#&*#n(#s &ns(an(#s Un r#,'*s*( a"*&*na% #s #% &n&*!*#n( "# %as &n"*&*n#s *n*&*a%#s a %a !*s!a ED S' !ar 3#n(aa sa%# a r#%'&*r &'an" %a f'n&*n #n %a 3ar*a.%# *n"#$#n"*#n(# ,'# a$ar# #n %a ED #s 'na f'n&*n s#&&*na"a C'an" s# r#s'#%3#n ED 'san" %a ()&n*&a "# %a (ransfr!a"as# &a!.*a 'na #&'a&*n "*f#r#n&*a% #n 'n $r.%#!a a%#.ra*& La !#("%7a &ns*s(# #n a$%*&ar %a (ransfr!a"a a %a ED $s(#r*r!#n(# 'sar %as $r$*#"a"#s "# %a (ransfr!a"a E% $r.%#!a "# a8ra &ns*s(# #n #n&n(rar 'na f'n&*n #n %a 3ar*a.%# *n"#$#n"*#n(# (#na 'na &*#r(a #9$r#s*n &! (ransfr!a"a
Denición de la Transformada S#a f 'na f'n&*n "#n*"a $ara Laplace "# f(t) s# "#n# &!
- %a transformada de
&'an" (a% *n(#ra% converge Notas 1 La %#(ra s r#$r#s#n(a 'na n'#3a 3ar*a.%#- ,'# $ara #% $rs "# *n(#ra&*n s# &ns*"#ra &ns(an(#
2 La (ransfr!a"a "# La$%a &n3*#r(# 'na f'n&*n #n t #n 'na f'n&*n #n %a 3ar*a.%# s : Cn"*&*n#s $ara %a #9*s(#n&*a "# %a (ransfr!a"a "# 'na f'n&*n; 1 D# r"#n #9$n#n&*a% 2 Cn(*n'a a (r<s Tabla de Transformadas 1 O.(#n&*n
2 O.(#n&*n
: O.(#n&*n
= O.(#n&*n Para n #n(#r ; 5 O.(#n&*n Para
N(a s.r# %a f'n&*n >a!!a 6 O.(#n&*n Para s > a
? O.(#n&*n
@ O.(#n&*n
O.(#n&*n
10
O.(#n&*n
Tabla de propiedades de la Transformada de Laplace