The ABC's of Resonance

Resonance causes an object to move back and forth or up and down. This motion is generally called oscillation. Sometimes the oscillation is easy to see such as the motion of a swing on a playground or the vibration in a guitar string. In other cases the oscillation is impossible to see without measuring instruments. For example,  electrons in an electrical circuit can oscillate but it happens on a molecular level. 

In resonance the oscillation occurs  at a specific frequency. These oscillations build up rapidly to very high levels. Ultimately some of the energy in the oscillations has to be removed from the object or the size of the oscillations get so large that the object breaks. 

Resonance requires 3 basic conditions:

A) An Object With a Natural Frequency: The object can be a mechanical device or an electronic circuit. An object's natural frequency is the frequency it tends to oscillate at when disturbed. The oscillation can be a mechanical vibration as is the case when the string of a guitar is strummed. In an electronic circuit the oscillation is a variable voltage or current. An object can have more than one natural frequency. These are called harmonics. A guitar string sounds musical because it vibrates with several harmonics when it is strummed.

B) A Forcing Function at the Same Frequency as the Natural Frequency: In mechanical systems the forcing function is a variable force. In electronic circuits it arises from a variable electric field. In either case the forcing function does work on the object it is applied to. Since work is a form of energy transfer it causes energy to build up in the object.

C) A Lack of Damping or Energy Loss: For an object to resonate, mechanical or electrical energy has to build up in the object. Anything which removes these forms of energy tends to interfere with resonance. Damping is a means of  removing electrical or mechanical energy by converting it to heat. The term damping should not be confused with the term dampening which means to make something slightly wet. Friction, air resistance, and viscous drag can all provide damping in mechanical systems. Electrical resistance performs the same function in electronic circuits. Other forms of energy loss can include sound (musical instruments) or light emissions (lasers).

When the forcing function's frequency  matches the natural frequency of an object it will begin to resonate. The forcing function adds energy at just the right moment during the oscillation cycle so that the oscillation is reinforced. This makes the oscillation's amplitude grow larger and larger. These oscillations would eventually become infinitely large. However, as mentioned earlier, long before the oscillations reach infinity one of three things happens: 1) the object's dynamics change so that the resonant frequency and forcing functions no longer match, 2) the energy lost as heat, sound, or light becomes equal to the energy input. or 3) the object breaks (see The Dark Side of Resonance).

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