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A table of laplace transforms for common functions, displaying both the time-domain function and the corresponding laplace domain function. Functions include exponentials, delays, derivatives, integrals, and sinusoids.
Typology: Exams
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Time-domain function Laplace domain function
f(t) F(s)
t
t u t s
s
f( t− τd ) e −s^ τdF(s)
t
2
s
dt
df sF^ (^ s)−f(^0 )
0
( )
t
1 F s( ) s
at e
−
s + a
at te
−
2 ( )
s + a
at e
t (^) −
2
2
3 ( )
s + a
τ
t
e
− 1 − ( 1 )
s τs +
2 2 ω
ω
s +
2 2
s
at e
−
2 2
s+ a +
at e −
2 2 ( + ) + ω
s a
s a
