Mechanical resonance
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Mechanical resonance is the tendency of a mechanical system to absorb more energy when the frequency of its oscillations matches the system's natural frequency of vibration (its resonant frequency) than it does at other frequencies. Examples are:-
- The acoustic resonances of musical instruments.
- The tidal resonance of the Bay of Fundy.
- Orbital resonance as in some moons of the solar system's gas giants.
- The resonance of the basilar membrane in the ear.
- Making a child's swing swing higher by pushing it at each swing.
- A wineglass breaking when someone sings a loud note at exactly the right pitch.
Resonance occurs in non-mechanical systems too: see resonance for more information.
A resonant object will probably have more than one resonant frequency, particularly at harmonics of the strongest resonance. It will vibrate easily at those frequencies, and less so at other frequencies. It will "pick out" its resonant frequency from a complex excitation, such as an impulse or a wideband noise excitation. In effect, it is filtering out all frequencies other than its resonance.
A swing set is a simple example of a resonant system that most people have practical experience with. It is a form of pendulum. If the system is excited (pushed) with a period between pushes equal to the inverse of the pendulum's natural frequency, the swing will swing higher and higher, but if excited it at a different frequency, it will be difficult to move. The resonant frequency of a pendulum, the only frequency at which it will vibrate, is given approximately, for small displacements, by the equation
where g is the acceleration due to gravity (about 9.8 m/s2 near the surface of Earth), and L is the length from the pivot point to the center of mass. (An elliptic integral yields a description for any displacement.) 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.
Resonance may cause violent swaying motions in improperly constructed bridges. Both the Old 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.
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.
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.
