# Second Order Systems

## Second Order Systems

A second-order system is one which can be described by a second-order differential equation.

The files listed below are a combination of PDF tutorial documents, 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 stand-alone 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.

Second-Order TheoryView File
Second-Order System Theory
Discussion of the system equation, homogeneous, and particular solutions for varying amounts of damping.
System Theory (pdf)
Second-Order Block Diagram Modeling
Construction of a block diagram of a second-order system, with an example model and response shown in Simulink.
Diagram Modeling (pdf)
Second-Order Initial Condition ResponseView File
Second-Order Initial Condition Response
Equations for and plots of system response to initial displacement, initial velocity, and combination,
for various amounts of damping.
Initial Condition Response (pdf)
M6.5 and M7.0 open in MATLAB, EXE is a stand-alone GUI
The user may input m, c, and k values for a second-order system and view the time response
of the system to an initial displacement of -1, the frequency response, and the root-locus.
GUI OverviewGUI Overview (pdf)
GUI AssignmentGUI Assignment (pdf)
LabVIEW not needed, zip file contains set-up for stand-alone GUI
This GUI allows the user to simulate the free response of a single-degree-of-freedom (SDOF), second-order 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.
LabVIEW
GUI OverviewGUI Overview (pdf)
GUI AssignmentGUI Assignment (pdf)
Second-Order Step ResponseView File
Second-Order Step Response
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.
Step Response (pdf)
M6.5 and M7.0 open in MATLAB, EXE is a stand-alone GUI
The user may input m, c, and k values of a second-order system, and
view the response of the system to a unit step, along with the frequency response and the root locus.
GUI OverviewGUI Overview (pdf)
GUI AssignmentGUI Assignment (pdf)
LabVIEW not needed, zip file contains set-up for stand-alone GUI
This GUI allows the user to simulate the step response of a single-degree-of-freedom (SDOF),
second-order 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.
LabVIEW
GUI OverviewGUI Overview (pdf)
GUI AssignmentGUI Assignment (pdf)
Second-Order Impulse ResponseView File
Second-Order Impulse Response
Definition of impulse, equations for and plots of system response for various levels of damping,
calculating impulse response in Simulink and MATLAB.
Impulse Response (pdf)
M6.5 and M7.0 open in MATLAB, EXE is a stand-alone GUI
The user may input m, c, and k values for a second-order system, and
then view the impulse response in the time domain, frequency domain, and root locus.
GUI OverviewGUI Overview (pdf)
GUI AssignmentGUI Assignment (pdf)
LabVIEW not needed, zip file contains set-up for stand-alone GUI
This GUI allows the user to simulate the impulse response of a single-degree-of-freedom (SDOF), second-order 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.
LabVIEW
GUI AssignmentGUI Assignment (pdf)
General Second-Order System ResponseView File
LabVIEW not needed, zip file contains set-up for stand-alone GUI
This GUI allows the user to simulate three different responses of a single-degree-of-freedom (SDOF), second-order 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.
LabVIEW
GUI OverviewGUI Overview (pdf)
GUI AssignmentGUI Assignment (pdf)
Second-Order Complex Frequency ResponseView File
M6.5 and M7.0 open in MATLAB, EXE is a stand-alone GUI The user can input m, c, and k values for a second-order system, and
view 5 plots describing the system: real and imaginary components of the FRF, magnitude, phase, and Nyquist.
GUI OverviewGUI Overview (pdf)
GUI AssignmentGUI Assignment (pdf)
S-Plane SurfaceView File
M6.5 and M7.0 open in MATLAB, EXE is a stand-alone GUI
The user may input m, c, and k values for a second-order system, and
choose to view one of 6 different plot types: 3D s-plane, phase plane, real plane, or imaginary plane, or
2D magnitude / phase or root locus.
GUI OverviewGUI Overview (pdf)
GUI AssignmentGUI Assignment (pdf)
Two Degree of Freedom System ResponseView File
Two Degree of Freedom Forced Vibration Theory
Discusses the theory behind modeling two degree of freedom systems
Theory (pdf)
LabVIEW not needed, zip file contains set-up for stand-alone 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.
LabVIEW
GUI Overview and AssignmentGUI Overview & Assignment (pdf)
Convolution IntegralView File
Convolution Theory
Discusses the theory behind the convolution integral
Convolution Theory (pdf)