Theory
 Initial Condition Response
 Step Response
 Impulse Response
System Response
 Complex Frequency Response
 SPlane Surface
Two
Degree of Freedom System

Convolution Integral
A
secondorder system is one which can be described by a
secondorder differential equation.
The
files listed below are a combination of PDF tutorial documents,
voice annotated tutorial documents (FLASH and AVI), MATLAB Graphical User Interfaces (GUIs), and LabVIEW GUIs. The
MATLAB GUIs are available for both MATLAB 6.5 and 7.0. In addition,
MATLAB .exe files are also available for those without MATLAB and can be used with the
MATLAB Runtime Engine.
See the general MATLAB GUI instruction file below for more
information on system requirements and how to run the
GUIs. The LabVIEW GUI .zip files
contain a standalone version which does not require LabVIEW to run.
See the readme in the .zip file for more information.
Each GUI .zip file contains a document of
suggested exercises to be performed with the GUI.
General MATLAB GUI
Instruction Download

PDF 
SecondOrder
Theory
SecondOrder System Theory

PDF 
Discussion of the system
equation, homogeneous, and particular solutions for varying amounts
of damping.

SecondOrder Block Diagram
Modeling

PDF 
Construction of a block
diagram of a secondorder system, with an example model and response
shown in Simulink.

SecondOrder
Initial Condition Response
SecondOrder Initial
Condition Response

PDF 
Equations for and plots of
system response to initial displacement, initial velocity, and
combination, for various amounts of damping.

MATLAB GUI Download

M6.5

M7.0

EXE

M6.5
and M7.0 open in MATLAB, EXE is a standalone GUI 
The
user may input m, c, and k values for a secondorder system and view
the time response of the system to an initial displacement of 1,
the frequency response, and the rootlocus.

GUI Overview

PDF

FLASH

AVI

GUI
Assignment

PDF

FLASH

AVI

FLASH  Streamed
(Requires Plugin) /
AVI  Non Streamed 
LabVIEW GUI Download

LabVIEW 
LabVIEW not needed, zip
file contains setup for standalone GUI 
This
GUI allows the user to simulate the free response of a
singledegreeoffreedom (SDOF), secondorder system. Mass, damping,
and stiffness are adjustable along with the initial conditions
necessary to provide the response. The time response, frequency
response, and root locus can be viewed.

GUI Overview

PDF 
FLASH 
AVI 
GUI Assignment

PDF 
FLASH 
AVI 
FLASH  Streamed
(Requires Plugin) /
AVI  Non Streamed 
SecondOrder
Step response
SecondOrder Step Response

PDF 
Definition of step function,
equations for and plots of system response for varying amounts
of damping, how to calculate step response in MATLAB and
Simulink.

MATLAB GUI Download

M6.5

M7.0

EXE

M6.5
and M7.0 open in MATLAB, EXE is a standalone GUI 
The
user may input m, c, and k values of a secondorder system, and view
the response of the system to a unit step, along with the frequency
response and the root locus.

GUI Overview

PDF

FLASH

AVI

GUI
Assignment

PDF

FLASH

AVI

FLASH  Streamed
(Requires Plugin) /
AVI  Non Streamed 
LabVIEW
GUI Download

LabVIEW 
LabVIEW not needed, zip
file contains setup for standalone GUI 
This
GUI allows the user to simulate the step response of a
singledegreeoffreedom (SDOF), secondorder system. Mass, damping,
and stiffness are adjustable along with the initial conditions and
step magnitude. The time response, frequency response, and root
locus can be viewed.

GUI Overview

PDF 
FLASH 
AVI 
GUI Assignment

PDF 
FLASH 
AVI 
FLASH  Streamed
(Requires Plugin) /
AVI  Non Streamed 
SecondOrder
Impulse Response
SecondOrder Impulse Response

PDF 
Definition of impulse,
equations for and plots of system response for various levels
of damping, calculating impulse response in Simulink and
MATLAB.

MATLAB GUI Download

M6.5

M7.0

EXE

M6.5
and M7.0 open in MATLAB, EXE is a standalone GUI 
The
user may input m, c, and k values for a secondorder system, and
then view the impulse response in the time domain, frequency domain,
and root locus.

GUI Overview

PDF

FLASH

AVI

GUI
Assignment

PDF

FLASH

AVI

FLASH  Streamed
(Requires Plugin) /
AVI  Non Streamed 
LabVIEW GUI Download

LabVIEW 
LabVIEW not needed, zip
file contains setup for standalone GUI 
This
GUI allows the user to simulate the impulse response of a
singledegreeoffreedom (SDOF), secondorder system. Mass, damping,
and stiffness are adjustable, along with the initial conditions and
impulse magnitude. The time response, frequency response, and root
locus can be viewed.

GUI Overview

PDF 
FLASH 
AVI 
GUI Assignment

PDF 
FLASH 
AVI 
FLASH  Streamed
(Requires Plugin) /
AVI  Non Streamed 
General
SecondOrder System Response
LabVIEW GUI Download

LabVIEW 
LabVIEW not needed, zip
file contains setup for standalone GUI 
This
GUI allows the user to simulate three different responses of a
singledegreeoffreedom (SDOF), secondorder system. Mass, damping,
and stiffness are adjustable, along with the initial conditions and
step or impulse magnitude. The time response, frequency response,
and root can be viewed.

GUI Overview

PDF 
FLASH 
AVI 
GUI Assignment

PDF 
FLASH 
AVI 
FLASH  Streamed
(Requires Plugin) /
AVI  Non Streamed 
SecondOrder
Complex Frequency Response
MATLAB GUI Download

M6.5

M7.0

EXE

M6.5
and M7.0 open in MATLAB, EXE is a standalone GUI 
The
user can input m, c, and k values for a secondorder system, and
view 5 plots describing the system: real and imaginary components of
the FRF, magnitude, phase, and Nyquist.

GUI Overview

PDF

FLASH

AVI

GUI
Assignment

PDF

FLASH

AVI

FLASH  Streamed
(Requires Plugin) /
AVI  Non Streamed 
SPlane Surface
MATLAB GUI Download

M6.5

M7.0

EXE

M6.5
and M7.0 open in MATLAB, EXE is a standalone GUI 
The
user may input m, c, and k values for a secondorder system, and
choose to view one of 6 different plot types: 3D splane, phase
plane, real plane, or imaginary plane, or 2D magnitude/phase or root
locus.

GUI Overview

PDF

FLASH

AVI

GUI
Assignment

PDF

FLASH

AVI

FLASH  Streamed
(Requires Plugin) /
AVI  Non Streamed 
Two Degree of Freedom System Response
Two Degree of
Freedom Forced Vibration Theory

PDF 
Discusses the theory behind modeling
two degree of freedom systems

LabVIEW
GUI Download

LabVIEW 
LabVIEW not needed, zip
file contains setup for standalone GUI 
This
GUI presents the response of a two degree of freedom system to
various inputs through the example of a unbalanced motor
attached to either degree of freedom.

GUI Overview and Assignment 
PDF 


Convolution Integral
Convolution
Theory

PDF 
Discusses the theory behind the
convolution integral

LabVIEW
GUI Download

LabVIEW 
LabVIEW not needed, zip
file contains setup for standalone GUI 
Two GUIs which present the convolution integral using both two
arbitrary signals and a SDOF system

GUI Overview and Assignment 
PDF 


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would greatly appreciate any feedback
you can provide to us about whether you have found this material
useful.
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