# Laplace Transform 4.

Cuthbert Nyack

## Pole Location

## Transfer Function

Pole locations and transfer function for a system with
2 pairs of complex conjugate
poles at a +- jb and c +- jd are shown above.

## Surface Plot of Magnitude of 4 poles

If you have Netscape 3.01 or other browser with a VRML viewer, then a 3-d
view of the magnitude, phase, real and imaginary parts of the Laplace
Transform of a system with 4 poles can be seen by clicking on one of
the links below. The values at the poles do go to infinity, but have been
truncated for convenience. The +ve imag axis coincides with the +ve z-axis
in the usual vrml coordinate system.
*MAGNITUDE*
*PHASE*
*REAL*
*IMAGINARY*

## Impulse and Step Response for a
system with 2 pairs of complex conjugate poles

Poles are at a + jb, a - jb, c + jd and c - jd. Horizontal axis
is 0 to 8pi when hgain = 1. Vertical axis is 0 to 2 for
step response and -1 to +1 for impulse response. Impulse
response is in red and step response in orange.

## Frequency Response for a
system with 2 pairs of complex conjugate poles

Horizontal is 0 to 8rad/s when hgain = 1. Vertical axis
for phase is -2p to
+2p and 0 to 2 for magnitude when
vgain is 1. Magnitude is red and Phase is
green.

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Copyright 1996 © Cuthbert A. Nyack.