A New Harmony: NIST Researchers Develop a Universal Method for Calculating the Resonances of Oscillators

A New Harmony: NIST Researchers Develop a Universal Method for Calculating the Resonances of Oscillators

Examples of harmonic motion in which objects oscillate at a resonance frequency. NIST researchers and their colleagues have developed a universal estimator to more accurately calculate the lowest possible uncertainty in measuring resonance frequencies, which play a key role in devices ranging from sensors to components in wireless communication.

Credit: K. Dill/NIST

The natural, or resonance, frequency at which a simple harmonic oscillator vibrates reveals with exquisite sensitivity the essential properties of the physical system to which it’s coupled. For instance, the resonance frequency of a guitar string indicates its length, mass, and tension. The resonance frequencies of miniature mechanical, acoustical, or optical harmonic devices can reveal such properties as the atomic-scale mass, motion, force, and acceleration of a system.

Resonance frequency measurements are integral to a host of scientific and commercial endeavors, from atomic force microscopy to high-precision, wireless communication, to the detection of single molecules. Resonators have even measured gravitational waves, disturbances in the geometry of space-time caused by the acceleration of massive objects.

Researchers are continually seeking ways to ensure they are measuring these frequencies with the highest accuracy possible. Yet until now, scientists had not developed a universal, fundamental way of understanding and estimating the uncertainties in measuring the resonance frequencies of harmonic oscillators.

Scientists at the National Institute of Standards and Technology (NIST) and their colleagues have calculated just how precisely scientists can measure the resonance frequencies of any harmonic oscillator – no matter what its physical properties. The calculation incorporates thermodynamic, quantum, and instrumental uncertainties, as well as whether a harmonic oscillation is driven by an external force or freely fluctuating, among a host of other factors.

NIST scientist Vladimir Aksyuk and his colleagues also derived a universal estimator for calc ..

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