# Laplace Transform of Step and Ramp

Cuthbert Nyack

To find the Laplace transform F(s) of a step function f(t) = 1 for
t ³ 0. Substitute f(t) into the definition of the Laplace Transform
below.
This gives the following:-
For a unit step F(s) has a simple pole at the origin.

To find the Laplace transform of a unit ramp f(t) = t for t ³ 0. Substitute f(t)
to give:-
Integrating by parts and evaluating gives:-
For a unit ramp F(s) has a double pole at the origin.

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Copyright 1996 © Cuthbert A. Nyack.