Anyone who has watched a child swinging on a playground swing has witnessed a vibrating system in resonance. The phenomenon of resonance appears often in everyday life; another example is the vibration of the body panels of a car containing a loud car stereo system. In the case of the child on the swing as the "vibrating system," resonance allows for fun and excitement, while in the case of the car stereo the resonance of the body panels is a source of annoyance. Three main concepts underlie vibrating systems and resonance: restoring force, natural frequency, and frequency matching.
A vibrating system is any system that exhibits a "restoring force." In the case of the child on a swing, the restoring force is the force of gravity that constantly acts to restore the swing to its place at the bottom of its arc. The force is called restoring because it always acts to restore the swing back to its vertical resting position. A restoring force results in vibration because any movement of the swing away from vertical will cause the swing to fall back towards vertical. In the case of the vibrating car panels the restoring force arises from the stiffness of the metal panels which forces the panels constantly towards the positions they were molded into by the manufacturer. Air pressure from the car stereo deforms the panels temporarily and causes them to vibrate around their molded positions.
Any system exhibiting a restoring force will possess a "natural frequency." In the case of the child on the swing the natural frequency is the number of swings undergone per second. Any swing has a natural frequency with which it tends to vibrate. This is intuitive when one considers that it would be disturbing to arrive at the playground and find the children swinging on the swings at the very low rate of one swing per hour, or the very fast rate of 100 swings per second! It seems the natural frequency of a child on a swing is somewhere near 1 swing per second. In fact, the natural frequency of a swing is largely determined by the length of the swing. Similarly, the body panels of a car have a natural frequency they "prefer" to oscillate at. These frequencies are higher than a swing's frequency, and are high enough that they can be heard as low tones or rattles.
Resonance appears when a vibrating system is forced to vibrate at its natural frequency. The child forces the swing to vibrate at its natural frequency by swinging her legs at the swing's natural frequency. This "frequency matching" causes the vibrations of the swing to grow large. The child exploits this phenomenon for fun and excitement. In the case of the car panels, when the stereo plays a note whose frequency corresponds to the natural frequency of a body panel, the body panel vibration will grow large. One might notice that different body panels will resonate with different played notes because each panel has a different resonant frequency. For the car owner, however, resonance is a source of annoyance and frustration.
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