6 Tabela de Transformadas de Laplace

Transformadas de Laplace Elementares

f(t) F (s) = L(f)(s) f(t) F (s) = L(f)(s)

11

s, para s > 0 eat

1

s − a, para s > a

cos ats

s2 + a2, para s > 0 sen at

a

s2 + a2, para s > 0

tn, para n ∈ Z+

n!

sn+1, para s > 0 eatf(t) F (s − a)

f ′(t) sF (s) − f(0) f ′′(t) s2F (s)−sf(0)−f ′(0)

t cos ats2 − a2

(s2 + a2)2, s > 0 t sen at

2as

(s2 + a2)2, s > 0

sen at − at cos at2a3

(s2 + a2)2, s > 0 δ(t − t0))(s) e−t0s, s > 0

ua(t) =

{

0, 0≤ t< a

1, t ≥ a

e−as

s, para s > 0 ua(t)f(t−a) e−asF (s)

f(t)δ(t − t0))(s) e−t0sf(t0), s > 0∫

t

0f(t − τ)g(τ)dτ F (s)G(s)

Tabela: Transformada de Laplace

11

s

eat1

s− a

tnn!

sn+1

senata

s2 + a2

cos ats

s2 + a2

senh ata

s2− a2

cosh ats

s2− a2

eatsenbtb

(s− a)2 + b2

eat cos bts− a

(s− a)2 + b2

tneatn!

(s− a)n+1

Uc(t)e−cs

s

Uc(t)f(t− c) e−csF (s)

ectf(t) F (s− c)

f(ct)1

cF

(s

c

)

∫

t

0

f(t− τ)g(τ)dτ F (s)G(s)

δ(t− c) e−cs

f (n)(t) snF (s)− s(n−1)f(0)− . . .− f (n−1)(0)

(−t)nf(t) F (n)(s)