numerical methods - 17.
1
17.
LAPLACE TRANSFORMS
17.
1 INTRODUCTION
Laplace transforms provide a method for representing and analyzing linear systems using algebraic methods.
In systems that begin undeflected and at rest the Laplace ’s’
can directly...
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numerical methods - 17.
1
17.
LAPLACE TRANSFORMS
17.
1 INTRODUCTION
Laplace transforms provide a method for representing and analyzing linear systems using algebraic methods.
In systems that begin undeflected and at rest the Laplace ’s’
can directly replace the d/dt operator in differential equations.
It is a superset of the phasor
representation in that it has both a complex part, for the steady state response, but also a
real part, representing the transient part.
As with the other representations the Laplace s is
related to the rate of change in the system.
Figure 17.
1 The Laplace s
The basic definition of the Laplace transform is shown in Figure 17.
2.
The normal
convention is to show the function of time with a lower case letter, while the same function in the s-domain is shown in upper case.
Another useful observation is that the transform starts at t=0s.
Examples of the application of the transform are shown in Figure 17.
3
for a step function and in Figure 17.
4 for a
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