This is a set of virtual experiments, consisting of a pendulum driven in one of four ways (sinusoidal force on the pendulum bob, and horizontal, vertical, and circular motion of the pivot point). The dynamical parameters of length, damping, driving amplitude, and driving frequency, can all be set over a wide range of possibilities.
Students can observe the pendulum motion with a virtual oscilloscope. The oscilloscope output can be selected between time, angle, and angular velocity. Different triggering options allow the display of the motion in a number of different modes, including a Poincare map.
An extensive collection of notes covering the theory of the system are also available.
Type of Material:
Java simulations with supporting text.
Recommended Uses:
Since this site is so extensive, it could be used as an interactive textbook. The applets can also be used in a lab setting or as an inclass activity or demonstration.
Technical Requirements:
This website does not work with I.E. 6.0.
Identify Major Learning Goals:
Study of equations of motion for oscillators, non-linear dynamics, and the wide range of phenomena possible in a relatively simple system.
Target Student Population:
Upper level undergraduate and graduate mechanics classes. Also of interest to both undergraduate modern physics classes and advanced topics classes covering chaos.
Prerequisite Knowledge or Skills:
Full use of this material, including the lecture notes, requires experience with partial differential equations and classical mechanics.
Content Quality
Rating:
Strengths:
The primary strength of this site is its completeness. This site contains all the information a student would need to study damped and driven oscillations.
The outstanding set of simulations will allow students to explore a wide range of physical phenomena experimentally. The simplicity of the system makes it immediately understandable to students. The range of parameter space that can be accessed makes this a powerful tool for helping students visualize and understand different phenomena.
The "Lecture" notes that are provided along with the simulations are outstanding. These explore the theoretical description of the system, including many of the more unusual and interesting behaviors due to the nonlinearities. Excellent use of of hyperlinking of this material makes it a joy to explore.
Concerns:
The lecture material is rather sophisticated, mathematically. Undergraduate students will probably need help handling this material.
The simulations can be started by dragging the pendulum to a certain angle with the mouse, but the initial angular velocity is always zero.
Potential Effectiveness as a Teaching Tool
Rating:
Strengths:
A strength of this material as a teaching tool is that the applets have the students use a "virtual oscilloscope" to take data instead of just giving them the period of osicillation, phase space maps, etc. These virtual experiments can be used in a way very similar to real lab experiments, although it would be difficult to set up the instrumentation to collect the data given by the simulation. Work with this material will be both hands-on and theoretical.
The experiments indicate regions of parameter space for students to study that show different sorts of physical behavior. This will focus the efforts of students and make their study productive.
The lecture material also includes questions for students to consider that will help them explore the theory presented.
Concerns:
Although the lecture notes very well written and broad, a text on mechanics and non-linear dynamics might be necessary for more in depth discussions.
Ease of Use for Both Students and Faculty
Rating:
Strengths:
This site is wonderfully crafted. The use of hyperlinks between experiment, theory, and definitions is masterfully done. The addition of an active site map at the top of each page is a welcome navigational tool.
The experiments themselves are simple and intuitive to run. The use of the oscilloscope by students will take some training, but the online help for this and all other operations of the applets will almost certainly cover any questions.
Concerns:
In the applets, the pendulum doesn't appear to change length when the length value of the pendulum is changed. This is only a small point as the physics seems to be correct.
This site currently does not work with Internet Explorer 6.0. The images do not show, and when one uses the "Back" navigation button on the browser, the html source appears rather than the rendered page. In addition, the applets do not run under the MS Java VM with IE 6, although they do work when the Sun 1.4 Java VM is used.
These problems do not occur with IE 5.5 and earlier, Netscape, or Mozilla.
Other Issues and Comments:
This is a uniquely well crafted site covering interesting and important physics.
Creative Commons:
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