[CSC 415] Pounds' Pendulum Particulars

[Andrew J. Pounds]

I know that some of you are working on your pendulum this weekend.  I 
was asked to provide some particulars to help guide you in your coding.

   1. You need one window with a pendulum that looks like a thin
      swinging beam.  This will be a 2D representation of a pendulum
      (nothing fancy -- think of a long rectangle moving around a point
      at one end).  The pendulum should move "physically" -- meaning
      that as it approaches the top of the window it is moving slower
      and has its maximum velocity when it swings through the bottom of
      the window.  Your window should be large enough to show the full
      motion of the pendulum so if you give it enough initial velocity,
      and it swings all the way around, you can see it.  I encourage you
      to start with the undamped case so you can carefully observe what
      is going on.  We will talk about input parameters this week.
   2. Your pendulum should move roughly at the same speed on any
      computer platform and graphics card (we will have to talk more
      about this in class -- you bascally will need to write "self
      tuning" graphics code).  Before you work on the tuning code, try
      to write your pendulum code so that the relative computer platform
      speed of the motion depends only on the step size "h" in the
      Runge-Kutta calculations.
   3. In a second window please show the
          * pendulum length
          * pendulum "bob" mass
          * initial velocity
          * an indicator showing if the motion is damped or undamped
          * if damped, the damping coefficient (or coefficient of
            friction). This can be combined with the damping indicator
            above.
          * the period of the pendulum (more about that later)
          * the instantaneous velocity in radians/sec
   4. You will need a third window in which you graph the phase space
      plot for the system as the pendulum motion is propagated.  We will
      talk about this more in class this coming week.
   5. As with projects in the past, I prefer that you make segemented
      source files with a single makefile to build the project.  If you
      intend to run your code on multiple platforms, then please include
      the appropriate information in the makefile to determine the type
      of platform on which you are building.  Use this information to
      call the appropriate sections of your makefile.
   6. Once you are done, I need everything tarred and gzipped and
      e-mailed to me.

Here are some question you might want to ask yourself.

   1. On what variable(s) does the pendulum's motion depend?
   2. If you run the pendulum undamped, is there some point at which it
      will cease to work properly?
   3. Can you give your pendulum the correct initial velocity to make it
      "hang" at the top?
   4. Does the period of the pendulum change as a function of time?
   5. Is there a relationship between the period of the pendulum and the
      Runge-Kutta stepsize "h"

-- 
Andrew J. Pounds, Ph.D.  (pounds at theochem.mercer.edu)
Associate Professor of Chemistry and Computer Science
Mercer University,  Macon, GA 31207   (478) 301-5627