Introduction to the Simulation

Parameters of the Pendulum

Throughout this lab you will be looking at a pendulum of length 10m and a mass of 50gm. The program will calculate the time evolution of the angle that the pendulum makes with the vertical, which we shall call Theta(t).

Getting Started

You will need to install the program "galileo" on your computer, or run it on a machine where it has already been installed.

The first thing that you want to do is to tell the program what your name is. Type your name in the box on the upper right. Your name will be included as the title on all the plots. Make sure to hit the Enter key after typing in your name (or changing any of the other entry boxes): if the box is still showing red, the computer hasn't read in the new value yet.

Now, notice the initial position of the pendulum. It should be tipped to the right; the sliders should show the initial angle Theta = 0.7 radians and the initial angular velocity Theta Dot = 0 radians per second.

Hit the button marked "Run". Observe the pendulum wiggle. Observe the graph of Theta versus Time on the right. By using the pull-down menu, change the plot from "Theta vs Time" to "Theta Dot vs Time", and "Energy vs Time". Notice the vertical scale on the last one. Why is the energy so flat?

Zoom in on a point on the plots by dragging on the right mouse button. (On a Mac, hold down the Control key while you click and drag.) Zoom out by clicking without dragging. Evaluate the coordinates of a point by clicking the left mouse button.

You can save the graph, combine graphs, print PostScript versions of the graphs, etc. using the "Copy Graph" button. See also the help for graphs. You'll want to fill in the box for ``Your Name'' first: graphs titled Waldo will usually not be accepted.

Run for a longer or a shorter time interval, using the "Time to Run" slider. Try sliding it to a longer time, and hit "Run". (If you slide too far, the simulation may take a very long time to finish. Just start over, making sure you type your name in again!) Type in a smaller value for the time, but be sure to hit Return to enter the new value.

Change the initial value of Theta to 0.1, and keep Theta Dot starting at zero. The animation looks even more boring than usual. Use the right button to zoom in on the green dot (details in the help for the animation), to see more of the motion.

Now try clicking with the left mouse button in the left-hand animation window, at where you want the green dot on the pendulum to start next. See that your initial value of Theta shows up on the slider too. (Zoom in on the plot of Theta vs Time to make sure it starts at the right place!)

Finally, try pushing the left mouse where you want to start the pendulum, and dragging to set the velocity. The length of the arrow denotes the value of ThetaDot (in arbitrary units).

Typing Quit will stop only after the current simulation ends.

Links Back

Statistical Mechanics: Entropy, Order Parameters, and Complexity, now available at Oxford University Press (USA, Europe).