Page 507 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

494 Introduction to Laplace Transformation Appen. B

TABLE B-1 SHORT TABLE OF LAPLACE TRANSFORMS

Hs) m
(1) S(l) = unit impulse at t « 0
(2) %,(/) “ unit step function at r —0

(3) -L(n= 1,2, • • • )
(n - I)!
(4)
s a
I
(5)
(i + a)
(6) 1 ;(/■ = 1,2, - • • ) I
(j + a)‘ {n- 1)!
1
(7) -(1 - e-^‘)
s(s + a)
1
(8)
5^(5 + a)
(9) cos at
5^ -I-
(10) cosh at
1 .

(11) —sin at

s a^
(12) —sinh at

a
(13) (1 —cos at)

5(5^+ Oi )

(14) (at - sin at)
+ a^ )

(15) — - (sin at — at cos at)
2^2
a^y 2a^
(16) sin at
,2 \2 2a
(17) t cos at
(S^ +
I
(18) f f"»' sin «0 V T - f ^
+ 2^0JfyS + 03q
<^oV 1 -