Resonance

:This article is about resonance in physics. For other senses of this term, see resonance (disambiguation).

Mechanics

A swing set is a simple example of a resonant system that most people have practical experience with. It is a form of pendulum, a type of resonant system. If you excite the system (push the swing) with a period between pushes equal to the inverse of the pendulum's natural frequency, the swing will swing higher and higher, but if you excite it at a different frequency, it will be very difficult. The resonant frequency of a pendulum, the only frequency at which it will vibrate, is given approximately, for small displacements, by the equation

Related Topics:
Swing set - Pendulum

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:f = {1 over 2 pi} sqrt {g over L}

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where g is the acceleration due to gravity (9.8 m/s2 for Earth), and L is the length from the pivot point to the center of mass. (The full equation is much more complicated, and leads to an elliptic integral.) Note that, in this approximation, the frequency does not depend on mass. A swing cannot easily be excited by harmonic frequencies, but can be excited by subharmonics.

Related Topics:
Acceleration due to gravity - Earth - Elliptic integral - Mass - Subharmonic

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Resonance may cause violent swaying motions in improperly constructed bridges. Both the Tacoma Narrows Bridge (nicknamed Galloping Gertie) and the London Millennium Footbridge (nicknamed the Wobbly Bridge) exhibited this problem. A bridge can even be destroyed by its resonance; that is why soldiers are trained not to march in lockstep across a bridge, but rather in breakstep.

Related Topics:
Tacoma Narrows Bridge - London Millennium Footbridge - Lockstep

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Mechanical resonators work by transferring energy repeatedly from kinetic to potential form and back again. In the pendulum, for example, all the energy is stored as gravitational energy (a form of potential energy) when the bob is instantaneously motionless at the top of its swing. This energy is proportional to both the mass of the bob and its height above the lowest point. As the bob descends and picks up speed, its potential energy is gradually converted to kinetic energy (energy of movement), which is proportional to the bob's mass and to the square of its speed. When the bob is at the bottom of its travel, it has maximum kinetic energy and minimum potential energy. The same process then happens in reverse as the bob climbs towards the top of its swing.

Related Topics:
Kinetic - Potential - Gravitational

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Other mechanical systems store potential energy in different forms. For example, a spring/mass system stores energy as tension in the spring, which is ultimately stored as the energy of bonds between atoms.

Related Topics:
Spring - Atom

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