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Periodic Motion: Two Connected Oscillators

In the last section we looked at a single oscillator moving in one dimension. Figure 11-7 shows a slightly more complicated system with two similar pendulums connected by a weak spring. Let's look at some general characteristics of this system.

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Figure 11-7

If one of the pendulums is set to swinging, the other pendulum hardly moves at first because the coupling is weak. Gradually, the second pendulum swings higher and higher, while the first pendulum swings less and less. Then the first pendulum comes almost to a stop while the second one swings with the original amplitude of the first. The energy of swinging has transferred from the first pendulum to the second. (See Figure 11-8.)

Now the situation is reversed from the original set up. The second pendulum now transfers energy to the first pendulum. This continues until the second one is at rest and the first is swinging.
This is an example of a general principle.
If two weakly connected oscillators have similar frequencies, and if the energy starts in one oscillator, then the energy tends to be slowly transfer back and forth between the oscillators. This is called resonance.


Figure 11-8 shows two pendulums with a very weak spring connecting them.

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Figure 11-8

Another example of resonance involves a soprano, a wine glass, and the air between them. The soprano can tap the glass to hear its natural frequency. If she sings that note very loudly, then the energy starts in one oscillator, her vocal cords, and transfers to the other oscillator, the wine glass, by the weak coupling, the air. In this case, enough energy enters the wine glass to cause it to go into a nonlinear regime, and it bursts. (See Section 7.E.)

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