9853

Free Response in a Second-Order System

This Demonstration can be used to study the free response of a second-order linear system. You can vary the system parameters (mass, damping, and stiffness) and simulate the response. The analytical solution is displayed at the top of the plot for the cases of underdamping, critically damping, and overdamp. In addition, a standard physical model of mass-spring-damper is run at the same time as the response plot is updated. You can set the initial conditions for initial position and speed using the sliders. Setting the initial conditions to and makes the response the same as the impulse response.

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

The underdamped response of a second-order system is given by . The critically damped system has the response and the overdamped system has the response . In all of the above, and can be found from the initial conditions, is the natural frequency in , is the damped natural frequency in , and is the damping coefficient.
For the underdamped case, the damped period of oscillation is given by and the time constant is given by ; both are in seconds. All units displayed are in SI.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2014 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+