Coupled Oscillations Applet A simulation that demonstrates the motion of oscillators coupled by springs
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Coupled Oscillations Applet Description

The oscillators (the "loads") are arranged in a line connected by springs to each other and to supports on the left and right ends. The mass of each load and the stiffness (spring constant) of each spring can be adjusted. At the top of the applet on the left you will see the string of oscillators in motion. By default, the number of loads is set to 5. To move the loads, click on one of them, drag it slightly to one side and then release it. Below the string you will see a graph showing each normal mode's contribution to the motion. There are two sets of terms; on top are the magnitude terms, which shows the amplitude of each normal mode, and on the bottom are the phase terms. Low-frequency modes are on the left and high-frequency modes are on the right. If you move the mouse over one of the modes, it will turn yellow, and the motion of the corresponding mode will be drawn underneath the line of oscillators in yellow (unless it's too small to see). So if you move the mouse over all the modes, you can see each of the terms individually. (One thing to keep in mind when looking at the magnitude of each mode is that the scale is not linear. If it were linear, it would look like the higher-frequency modes all had zero magnitude because their contribution is so small. For small magnitudes, the scale is logarithmic; then about 1/4 of the way up the scale it switches to linear. The same is true for negative magnitudes.) You can modify the motion of the string in one of two ways. You can click on it directly, or you can modify the normal modes. Take Coupled Oscillations Applet for a spin to see what it's really capable of!

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