Nonlinear 
Oscillations
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HOW TO USE THE SOFTWARE

Each simulation program of the package is supplied with several sets of predefined examples illustrating many interesting modes of the simulated system behavior. To open the list of examples, click on the button "Demo Examples" on the title screen, or on the menu item "Examples" which can be found in the upper line of any screen, or in the pop-up menu called by clicking the right mouse button. It might be a good idea to begin your work with a program by looking through these examples in a survey mode. In this mode, you need not enter data or choose options. The image of the simulated system on the display screen is intentionally made to appear very schematic to remind you that in the simulation experiment you are dealing not with a real physical system but rather with some idealized model of it.

Additional background material explaining the simulated physical systems and different modes of their behavior can be found in text documents and articles (pdf files) that supplement almost all programs of the package. You will need Adobe Acrobat Reader program to read papers and other text documents of the package. These materials are available directly from the programs by clicking Help on physics" in the menu. Some of the papers have been published in the literature. You can read the papers (and print them out) directly from here:

HOW TO CONTROL THE PROGRAMS

To perform various controlling functions, using the mouse is very convenient. You simply click on control buttons or menu items, or you drag the slides on scroll-bars. Clicking the mouse right button, you call the context-sensitive pop-up menus.

Clicking the menu item "View allows you to choose one of the four (or more) screen configurations, which differ by the amount of information displayed:

  • Image of the physical system with the timer (only);
  • ... plus the plots of time dependence of the angular displacement and of the angular velocity;
  • ... plus the phase diagram;
  • ... plus the plots of energy transformations.

Command buttons and screen controls in all parts of the programs perform the following functions:

  • Start, Pause – begin the simulation, pause, resume;
  • Restart – restore the initial values and resume the simulation;
  • Change – call up the control panel to change properties;
  • Erase – remove the old plots (and rescale) before going on;
  • Options – call up the control panel to choose options;
  • Exit – return to the starting page of the program;
  • Skip Over – skip the simulation over several periods of the external action (the desired number of periods you can type into the box);
  • Time Scale – change the number of periods displayed on the plots;
  • Animation – speed up or slow down the animation.

To change properties of the physical system (such as the quality factor, the frequency and amplitude of the external action, etc. – depending on the system under consideration) or the initial conditions (values of the angular displacement and angular velocity at t = 0), click on the button Change or the item "Settings" in the menu. A control panel then appears in which you can type in the new values in corresponding dialog boxes, or you can change the values by dragging the slides on the scroll-bars. When all chosen values are specified, confirm your choice by clicking the OK button. Or click the Cancel button, if you wish to ignore the changes and return to the previous values.

If you click the button Options or the menu item "Options," a control panel appears from which you can choose a mode of simulation and a mode of displaying information which best fits your requirements:

  • You can choose one of three option buttons in plotting functions:
    • the program is to pause in the simulation when all the space for the plots is used and is to wait for your next command, or
    • it should continue drawing new plots over the old ones or
    • it should erase them before continuing plotting.
  • You can choose the thickness of lines for drawing the plots, and the background color (dark or white) by checking the switches;
  • If you wish to suppress the automatic choice of scale and to choose your own scale, select the option "Custom Scale" and indicate the maximal values of the angular displacement and angular velocity to be displayed on the plots.

The software allows you to make a hard copy of the plots with the help of your system printer. The plots will have the best resolution which your printer can provide. To print the plots, perform the following steps:

  • Input, if necessary, the values of parameters and initial conditions (the plot will correspond to the current values of the system parameters);
  • Choose the menu item File, Print. A printer control panel will appear;
  • In the panel, choose the plot you wish to print (angular displacement or angular velocity time dependence, phase diagram, or energy transformations) by clicking the corresponding option button;
  • Input the plot dimensions (width and height) in the units you are used to (inches, centimeters, pixels, or points). The program will round out the values in order to get the best result on your printer;
  • Select the time interval for the plot: indicate the number of the natural periods (or the external force periods, or the periods of modulation, depending on the program) to be reproduced (time scale), and the initial instant of the time interval;
  • If you wish, you can add a caption to the plot (type its text into the corresponding box), and a header (for the whole page where you can print several plots);
  • Choose whether or not to print the legend and the values of parameters (under the plot);
  • Click the Go command button after all the necessary settings have been made.

After the image of the plot is stored in the computer's memory (the label "Wait..." will change to the label "Ready"), you can choose several possibilities to continue:

  • Get a hard copy of the plot by clicking the Eject command button. Only one plot will be printed out;
  • If you click the More command button, then the next part of the process (one more interval ordered in the box "Time Scale") will be placed over the same plot (together with the previous part);
  • You can store another plot image in order to print it below on the same sheet of paper. To do this, repeat the previous steps and make the settings for the second plot. The program will warn you if free space on the sheet is insufficient for the next plot;

Click on the Eject command button to send all the stored images to the printer.

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Nonlinear Oscillations – a Virtual Lab