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What Are Forced Oscillations?

Tree branches swaying in the wind, waves lapping at a shore, a rubber ball bouncing down a sidewalk -- these are all examples of oscillations. Our lives -- indeed, our selves -- are filled with oscillations. From the sound that fills the air to the chemicals that fill our bodies, systems that oscillate are everywhere. Sometimes, the systems just respond to an impulse, then oscillate freely, but sometimes, something pushes the oscillating system. That's a forced oscillation.

Equilibrium
- All oscillations occur in a system that has some balance point, or equilibrium point. A swing, for example, is perfectly balanced when it is hanging straight down. When the swing is disturbed from equilibrium, it responds to what is called a "restoring force." A restoring force is just what it sounds like: a force that tries to bring back, or restore, the equilibrium of the system. Pull the swing back and let it go and it will move forward, but it has extra energy that pushes it right past equilibrium; then the force starts pushing it backward. And so on. Oscillation.
Free Oscillation
- If you give one push on a swing, it will go forward and back at a fixed rate, a rate that depends upon its length. A clock pendulum does the same thing. A piano string struck by a hammer, a rock tossed in a pool, a rubber ball rolled from a table -- these are all examples of a system that is displaced from equilibrium by a single quick impulse. After the impulse, the oscillation of the system proceeds without external help. The frequency of the oscillation depends only on the characteristics of the system. That's called free oscillation.
Forced Oscillation
- Pushing a swing at its natural frequency creates the biggest response.
  
  What if, instead of just giving the swing one push, you give it a push every two seconds? The motion of the swing will now depend not only on the length of the swing, but also on the frequency and strength with which you're pushing. The same is true for any forced oscillation. The motion of a system in response to the applied force doesn't depend just on the system's characteristics, as in free oscillation. Now it's a function of the system and of the applied force.
Resonance
- The most interesting kinds of forced oscillation take place when the frequency of the applied force matches the natural frequency of the system. When a force matches the natural frequency, it creates a condition called "resonance." When you're pushing a swing, you naturally apply the force at the resonant frequency, pushing each time the swing starts forward again. You know that's the way to get the biggest response from the swing. The same kind of behavior is seen in every forced oscillation. The largest response from the system comes when it is pushed near resonance. This is true for everything from playground swings to radio receivers.

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