function f(t) 1 tn eat sin at cos at sinh at cosh at e-at f(t) - U(t a) or Ua(t) (a ≥ 0) 8(ta) (a>0) - Laplace transform F(s) 1/s (s>0) n!/sn+1 (s>0) 1/(sa) (sa) a/(s²+a²) (s> 0) s/(s²+a²) (s> 0) a/(s² – a²) (s>|a|) s/(s² – a²) (s> |a|) F(s+a) -as e as e U(t − a) ƒ (t − a) or U₁(t) ƒ (t − a) as - e f(n) (t) (−t)" f(t) (f*g)(t) = f ƒ (7)g(t − T) dà - $/s (s> 0) F(s) s"F(s) – sn−¹ƒ(0) — sn−² ƒ' (0) · · F(n) (s) F(s)G(s) · f(n−1) (0) F(s) = (54*(2s+12))/(s^2+12s+117)^2 f(t) = 6te sin(9+)
function f(t) 1 tn eat sin at cos at sinh at cosh at e-at f(t) - U(t a) or Ua(t) (a ≥ 0) 8(ta) (a>0) - Laplace transform F(s) 1/s (s>0) n!/sn+1 (s>0) 1/(sa) (sa) a/(s²+a²) (s> 0) s/(s²+a²) (s> 0) a/(s² – a²) (s>|a|) s/(s² – a²) (s> |a|) F(s+a) -as e as e U(t − a) ƒ (t − a) or U₁(t) ƒ (t − a) as - e f(n) (t) (−t)" f(t) (f*g)(t) = f ƒ (7)g(t − T) dà - $/s (s> 0) F(s) s"F(s) – sn−¹ƒ(0) — sn−² ƒ' (0) · · F(n) (s) F(s)G(s) · f(n−1) (0) F(s) = (54*(2s+12))/(s^2+12s+117)^2 f(t) = 6te sin(9+)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:function f(t)
1
tn
eat
sin at
cos at
sinh at
cosh at
e-at f(t)
-
U(t a) or Ua(t) (a ≥ 0)
8(ta) (a>0)
-
Laplace transform F(s)
1/s (s>0)
n!/sn+1 (s>0)
1/(sa) (sa)
a/(s²+a²) (s> 0)
s/(s²+a²) (s> 0)
a/(s² – a²) (s>|a|)
s/(s² – a²) (s> |a|)
F(s+a)
-as
e
as
e
U(t − a) ƒ (t − a) or U₁(t) ƒ (t − a)
as
-
e
f(n) (t)
(−t)" f(t)
(f*g)(t) = f ƒ (7)g(t − T) dÃ
-
$/s (s> 0)
F(s)
s"F(s) – sn−¹ƒ(0) — sn−² ƒ' (0) · ·
F(n) (s)
F(s)G(s)
· f(n−1) (0)
Transcribed Image Text:F(s)
= (54*(2s+12))/(s^2+12s+117)^2
f(t) = 6te sin(9+)
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