Baixe o app para aproveitar ainda mais
Prévia do material em texto
TRANSFORMADA DE LAPLACE DE ALGUMAS FUNÇÕES 1 f (t) L{ f (t)} 1 1s t 1s2 tn n!sn+1 tα Γ(α+1)sα+1√ t √ pi 2 √ s3 1√ s √ pi s sen(kt) ks2+k2 cos(kt) ss2+k2 sen2(kt) 2k 2 s(s2+4k2) cos2(kt) s 2+2k2 s(s2+4k2) eat 1s−a senh(kt) ks2−k2 cosh(kt) ss2−k2 senh2(kt) 2k 2 s(s2−4k2) cosh2(kt) s 2−2k2 s(s2−4k2) teat 1(s−a)2 tneat n!(s−a)n+1 tsen(kt) 2ks(s2+k2)2 tcos(kt) s 2−k2 (s2+k2)2 eatsen(kt) k(s−a)2+k2 eatcos(kt) s−a(s−a)2+k2 tsenh(kt) 2ks(s2−k2)2 tcosh(kt) s 2+k2 (s2−k2)2 eatsenh(kt) k(s−a)2−k2 f (t) L{ f (t)} eatcosh(kt) s−a(s−a)2−k2 eat−ebt a−b 1 (s−a)(s−b) aeat−bebt a−b s (s−a)(s−b) cos(bt)−cos(at) a2−b2 s (s2+a2)(s2+b2) sen(kt) · senh(kt) 2k2ss4+4k4 sen(kt) · cosh(kt) k(s2+2k2)s4+4k4 cos(kt) · senh(kt) k(s2−2k2)s4+4k4 cos(kt) · cosh(kt) s3s4+4k4 ebt−eat t ln ( s−a s−b ) sen(at) t arctg ( a s ) sen(at)·cos(bt) t 1 2arctg ( a+b s ) + 12arctg ( a−b s ) 2−cos(at) t ln ( s2+k2 s2 ) 2−cosh(at) t ln ( s2−k2 s2 ) δ(t) 1 δ(t− t0) e−s t0 eat f (t) F(s−a) Ua(t) e−ass f (t−a) ·Ua(t) e−as ·Fs f (n)(t) snF(s)− sn−1 f (0)− · · ·− f (n−1)(0) tn f (t) (−1)n dndsnF(s) t∫ 0 f (α)g(t−α)dα L{ f (t)} ·L{g(t)} t∫ 0 f (α)dα L{ f (t)}s 1disponível em www.ceunes.ufes.br/prof/wescleybonomo
Compartilhar