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The primary difference between a computer algebra system and a traditional calculator is the ability to deal with equations symbolically rather than numerically. The precise uses and capabilities of these systems differ greatly from one system to another, yet their purpose remains the same: manipulation of symbolic equations .
Increase of amplitude as damping decreases and frequency approaches resonant frequency of a driven damped simple harmonic oscillator. [1] [2]Resonance is a phenomenon that occurs when an object or system is subjected to an external force or vibration that matches its resonant frequency, defined as the frequency that generates the maximum amplitude response in the system.
Mechanical resonance is the tendency of a mechanical system to respond at greater amplitude when the frequency of its oscillations matches the system's natural frequency of vibration (its resonance frequency or resonant frequency) closer than it does other frequencies. It may cause violent swaying motions and potentially catastrophic failure in ...
The free motion described by the normal modes takes place at fixed frequencies. These fixed frequencies of the normal modes of a system are known as its natural frequencies or resonant frequencies. A physical object, such as a building, bridge, or molecule, has a set of normal modes and their natural frequencies that depend on its structure ...
One key advantage of the LGR is that, at its resonant frequency, its dimensions are small compared to the free-space wavelength of the electromagnetic fields. Therefore, it is possible to use LGRs to construct a compact and high-Q resonator that operates at relatively low frequencies where cavity resonators would be impractically large.
All diagonal elements in a tuned filter are equal to zero because a susceptance vanishes at the resonant frequency. Important merit of the matrix M {\displaystyle \mathbf {M} } is the fact that it allows to directly compute the frequency response of the equivalent network having the inductively coupled resonant circuits,.
A Laplace resonance is a three-body resonance with a 1:2:4 orbital period ratio (equivalent to a 4:2:1 ratio of orbits). The term arose because Pierre-Simon Laplace discovered that such a resonance governed the motions of Jupiter's moons Io , Europa , and Ganymede .
In effect, it is filtering out all frequencies other than its resonance. Acoustic resonance is an important consideration for instrument builders, as most acoustic instruments use resonators, such as the strings and body of a violin, the length of tube in a flute, and the shape of a drum membrane. Acoustic resonance is also important for hearing.