s
1 2
L[(t - Ä…t )e-Ä…t] =
2 3
(s +Ä…)
s2
1 2
L[(1-2Ä…t + Ä…2t )e-Ä…t ] =
2 3
(s +Ä…)
Tablica transformat Laplace a L[´ (t)] =1
L[af (t) + bg(t)] = aF(s) + bG(s)
É
2
L[´ (t)] = s
n
L[sin Ét] =
îÅ‚
d
( n-1)
s2 +É2
2
L f (t)Å‚Å‚ = snF(s) - sn-1 f (0-) - sn -2 f (0-) -... - f (0-)
n
ïÅ‚dt śł
n
îÅ‚ Å‚Å‚
d
ðÅ‚ ûÅ‚
s
L ´ (t)śł = sn
ïÅ‚dt
n
L[cosÉt] =
ðÅ‚ ûÅ‚
t
îÅ‚ Å‚Å‚ s2 +É2
F(s)
0
L f
ïÅ‚
L[´ (t -t0 )] = e-st , t0 e" 0
+"(Ä)dÄ śł = s É
L[e-Ä…t sin Ét] =
ïÅ‚ śł
ðÅ‚0- ûÅ‚
2
n
îÅ‚ Å‚Å‚ (s +Ä…) +É2
d
0
L ´ (t - t0 )śł = sne-st , t0 e" 0
L[e-Ä…t f (t)] = F(s +Ä…)
ïÅ‚dt
n
s +Ä…
ðÅ‚ ûÅ‚
n L[e-Ä…t cosÉt] =
2
d
(s +Ä…) +É2
1
L[tn f (t)] = - F(s)
L[1(t)] =
dsn
s
1 1
îÅ‚
"
L (1-cosÉt)Å‚Å‚ =
f (t)
îÅ‚ Å‚Å‚ ïÅ‚É2 śł
1
0 s(s2 +É2)
ðÅ‚ ûÅ‚
L = F(s)ds
L[1(t - t0 )] = e-st
+"
ïÅ‚ śł
t
ðÅ‚ ûÅ‚
s
s
t s
îÅ‚ Å‚Å‚
L sin Étśł =
0 1
ïÅ‚2É ûÅ‚ 2
L[ f (t - t0)1(t - t0)] = F(s)e-st
L[t] =
ðÅ‚
(s2 +É2)
s2
îÅ‚ t Å‚Å‚
ëÅ‚ öÅ‚
2És
n
L f =Ä…F(Ä…s)
ìÅ‚ ÷łśł
îÅ‚ Å‚Å‚ L[t sin Ét] =
t 1
ïÅ‚
2
L =
íÅ‚Ä… Å‚Å‚
ðÅ‚ ûÅ‚
ïÅ‚
(s2 +É2)
n!śł sn+1
ðÅ‚ ûÅ‚
L[ f (t) " g(t)] = F(s)G(s)
s2 -É2
1
L[t cosÉt] =
L[e-Ä…t] = 2
1
(s2 +É2)
L[ f (t)g(t)] = G(s) " F(s)
s +Ä…
2Ä„j
1 ²
L[te-Ä…t ] =
" L[sh ²t] =
2
2
îÅ‚ F1(s)
(s +Ä…) s2 - ²
L f (t) = f1(t - kT )Å‚Å‚ =
"
ïÅ‚ śł
1 - e-sT
ðÅ‚ k =0 ûÅ‚ n
s
îÅ‚ Å‚Å‚
t e-Ä…t 1
L[ch ²t] =
L =
2
ïÅ‚ śł
n-1
s2 - ²
n!
(s +Ä…)
ðÅ‚ ûÅ‚
²
1 1
îÅ‚
L[e-Ä…t sh ²t] =
L (1- e-Ä…t )Å‚Å‚ = 2
2
ïÅ‚Ä… śł
(s +Ä…) - ²
s(s +Ä…)
ðÅ‚ ûÅ‚
s +Ä…
s
L[e-Ä…t ch ²t] =
L[(1-Ä…t)e-Ä…t] =
2
2
2
(s +Ä…) - ²
(s +Ä…)
2²s
îÅ‚ 1 1
L[t sh ²t] =
L (e-Ä…t - e-²t )Å‚Å‚ = 2
2
ïÅ‚² -Ä… śł
(s2 - ² )
(s +Ä…)(s + ²)
ðÅ‚ ûÅ‚
2
s2 + ²
îÅ‚ 1 s
L[t ch ²t] =
L (Ä…e-Ä…t - ²e-²t )Å‚Å‚ =
2
ïÅ‚Ä… - ² śł 2
(s +Ä…)(s + ²) (s2 - ² )
ðÅ‚ ûÅ‚
2É2
1 1
îÅ‚
L[sin2 Ét] =
L (e-Ä…t +Ä…t -1)Å‚Å‚ =
ïÅ‚Ä… 2
śł
s2(s +Ä…) s(s2 + 4É2)
ðÅ‚ ûÅ‚
1 1 s2 + 2É2
îÅ‚
L [1-(1+Ä…t)e-Ä…t]Å‚Å‚ = L[cos2 Ét] =
ïÅ‚Ä… 2 2
śł
ðÅ‚ ûÅ‚ s(s +Ä…) s(s2 + 4É2)