Instructions for the applet:
The applet given is a simulation of a linear driven damped oscillator. The heavy line connecting the motor and the blue ball is a bungee cord or a spring. The blue ball is a mass on the spring. The natural frequency of the system has been calculated for you (sqrt(k/m)). The ball is moving in water whose resistive force we can alter using the appropriate text box below the graph. (Perhaps we are adding gelatin to it or something.) The water acts like a damping force on the spring system. The motor shakes the spring at a frequency given by the appropriate text box below the graph.
**Important note: although the spring system is "vertical", the force of gravity has NOT been added to the simulation.**
The applet plots the position versus time of the blue ball. The output is a sine wave. In the questions below you will be asked to find the amplitude of the sine wave for various driving frequencies.
Troubleshooting
- You should type in only the numbers (e.g. 1.0 and 2.0) without the units (do not type "1.0 rad/s"). The units are already accounted for. Doing so will not crash the program but will result in values which do not change.
- You will need to install the java plug-in to run the program. You cannot run the program without it. The program will direct you to Sun's website if you do not have the plug in.
- The Java plug-in is not normally self-installing. Make sure you have double clicked on the box icon which you downloaded. You should have gone through an "Install shield" if you have properly installed the plug in.
- (!!) Mac users CANNOT run this applet unless they have OS X.
- You will need Internet Explorer 5 or above -or- Netscape 4.7 or above.
- If all else fails, GO TO the computer in the study room (Wat 421) I will make sure that the program runs on it.
Questions:
Make two graphs: (note that they are not supposed to be symmetric)
- Graph 1: Amplitude versus driving frequency, damping constant 0.5 1/s
- Leaving the damping constant at 0.5, determine the amplitude of the oscillations at the driving frequencies 4.0, 3.0, 2.5, 2.0, 1.5, 1.0 rad/s
- Graph 2: Amplitude versus driving frequency, damping constant 1.0 1/s
- Change the damping constant to 1.0, determine the amplitude of the oscillations at the driving frequencies 4.0, 3.0, 2.5, 2.0, 1.5, 1.0 rad/s