Mechanical resonance

Mechanical resonance happens when a system vibrates with a much larger amplitude because the frequency driving it matches its own natural frequency. This can lead to violent shaking and even catastrophic collapse in poorly built structures like bridges, buildings, or aircraft—a problem called resonance disaster.

Avoiding such disasters is a key concern in construction. For example, Taipei 101 uses a 660-ton pendulum, called a tuned mass damper, to change how it responds at resonance, and the building is also designed to resonate at a frequency that rarely occurs. In earthquake zones, buildings are often built to account for the expected ground motion frequencies. Engineers also make sure that the resonant frequencies of engine parts don't match the vibrations from motors or other oscillating components.

Many resonant objects have more than one resonant frequency. They vibrate easily at those frequencies and much less at others. Many clocks keep time using mechanical resonance in a balance wheel, pendulum, or quartz crystal.

The natural frequency of a simple spring-and-mass system is given by f = (1/2π)√(k/m), where m is mass and k is the spring constant. For a given mass, making the system stiffer (increasing k) raises its natural frequency—a general rule for vibrating mechanical systems.

A swing set is a familiar example of a resonant system, a type of pendulum. If you push it with a period matching the inverse of its natural frequency, it swings higher and higher. Push at a different frequency, and it's hard to move. For small displacements, a pendulum's resonant frequency is approximately f = (1/2π)√(g/L), where g is gravity (about 9.8 m/s²) and L is the length from pivot to center of mass. In this approximation, frequency doesn't depend on mass.

Mechanical resonators work by repeatedly transferring energy between kinetic and potential forms. In a pendulum, all energy is stored as gravitational potential energy when the bob is motionless at the top of its swing. This energy depends on the bob's mass and its height above the lowest point. As the bob descends, potential energy converts to kinetic energy, which depends on mass and the square of speed. At the bottom, kinetic energy is highest and potential energy lowest. The process reverses as the bob climbs back up.

Some resonant objects have multiple resonance frequencies, especially at harmonics (multiples) of the strongest one. They vibrate easily at those frequencies and less at others. They "pick out" their resonant frequency from a complex excitation, like an impulse or wideband noise—effectively filtering out all other frequencies. A swing, for instance, isn't easily excited by harmonics but can be excited by subharmonics, like pushing every second or third swing.

Examples of mechanical resonance include musical instruments (acoustic resonance), most clocks (using balance wheels, pendulums, or quartz crystals), tidal resonance in the Bay of Fundy, orbital resonance in some giant-planet moons, the resonance of the basilar membrane in the ear, and a wineglass breaking when a loud note hits exactly the right pitch. Resonance can also cause violent swaying in structures like bridges and buildings—the London Millennium Footbridge (the Wobbly Bridge) had this problem. A faulty bridge can even be destroyed by resonance (see Broughton Suspension Bridge and Angers Bridge). Mechanical systems store potential energy in different forms; for example, a spring-mass system stores energy as tension in the spring, ultimately as energy between atoms.

A resonance disaster in mechanics and construction describes the destruction of a building or mechanism by induced vibrations at its resonant frequency. Periodic excitation optimally transfers vibrational energy into the system and stores it there. With repeated storage and added energy, the system swings more and more strongly until its load limit is exceeded.