Physics in Action: Resonance

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It is a very fundamental concept in physics that most systems have a natural frequency. What does that mean? Suppose we consider these two simple pendulums, balls on the end of the string. Suppose I pull this out and let it go. If I don't touch it all and let it move, it swings at a frequency that is determined. I'm not telling it which frequency to move at. If I pull this ball out, notice that it moves at a different frequency, a much slower frequency than the first one. If I pull them out together, you can see this very clearly. I'll start from this position, pull them out and release them at the same time. You see very clearly that the ball on the end of the shorter string is moving back and forth a lot faster than the ball on the end of the longer string. With this system--namely, a mass on the end of the string, idealized--the natural frequency is determined only by the length of the string, and that's it. Balls handing from strings of different lengths will have different natural frequencies, as you've just seen.
Now, when a system has a natural frequency, it sets up this phenomenon of resonance. If I push a system at its natural frequency, I can transmit energy from this thing that is doing the pushing to the this thing that is receiving the push, in a very efficient way. That phenomenon is called resonance.
Suppose this ball was actually a swing, and I'm pushing my child on a swing in the park. I might pull him back, release the swing, and it will start pushing it at exactly the frequency that it wants to go. We all know that if we do this, push the swing at exactly the right frequency, we can make it move very, very far. If I push the swing like this and keep pushing it in the right way, the amplitude--namely, how far it swings back and forth--can be very, very large. If I do it the right way; that is an example of the phenomenon of resonance.
Let's see that with this demonstration over here. We have a series of eight balls hanging by strings of different lengths on this rod. Now let's see what happens if I pull back this yellow ball over here. I have two yellow balls and six red balls. Let's watch the yellow balls very carefully.
Notice what's happening. I pulled back only this yellow ball over here, and the only other ball to respond in a significant way is the other yellow ball. When I pulled back this yellow ball, note that it's connected by means of a string to this red bar, but this red bar is not fixed. It rocks a little bit, which I can see in the following way. When this yellow ball goes back and forth, it actually pushes the red bar back and forth, and that red bar pushes all of the balls back and forth, as you can see in this exaggerated motion that I'm doing. However, when I pull this yellow ball back and forth and cause this red bar to go back and forth at the natural frequency of this yellow ball, that natural frequency matches the natural frequency of only one other ball in this whole array, and that is the other yellow ball. So when I drive, by means of this yellow ball, the bar and all the other balls, this ball is one that's going to pick up energy most efficiently. That is the phenomenon of resonance.
Let's see that one more time. I bring all the balls to rest. Again we see that the ball, which picked up the most energy from the yellow ball that I pulled back was the other yellow ball, because it has the same natural frequency as the original yellow ball. This is the phenomenon of resonance.
Oscillatory Motion
Damped and Driven Oscillations
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