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A molecular vibration is a periodic motion of the atoms of a molecule relative to each other, such that the center of mass of the molecule remains unchanged. The typical vibrational frequencies range from less than 10 13 Hz to approximately 10 14 Hz, corresponding to wavenumbers of approximately 300 to 3000 cm −1 and wavelengths of approximately 30 to 3 μm.
In Wilson's GF method it is assumed that the molecular kinetic energy consists only of harmonic vibrations of the atoms, i.e., overall rotational and translational energy is ignored. Normal coordinates appear also in a quantum mechanical description of the vibrational motions of the molecule and the Coriolis coupling between rotations and ...
A vibration powered generator is a type of electric generator that converts the kinetic energy from vibration into electrical energy. The vibration may be from sound pressure waves or other ambient vibrations. Vibration powered generators usually consist of a resonator which is used to amplify the vibration source, and a transducer mechanism ...
As specific examples, the linear CO 2 molecule has 4 modes of oscillation, [5] and the nonlinear water molecule has 3 modes of oscillation [6] Each vibrational mode has two energy terms: the kinetic energy of the moving atoms and the potential energy of the spring-like chemical bond(s).
In order to obtain a Hamiltonian for external (translation and rotation) motions coupled to the internal (vibrational) motions, it is common to return at this point to classical mechanics and to formulate the classical kinetic energy corresponding to these motions of the nuclei.
By conservation of energy, assuming the datum is defined at the equilibrium position, when the spring reaches its maximal potential energy, the kinetic energy of the mass is zero. When the spring is released, it tries to return to equilibrium, and all its potential energy converts to kinetic energy of the mass.
Kinetic energy of a regulation baseball thrown at the speed of the Oh-My-God particle, itself a cosmic ray proton with the kinetic energy of a baseball thrown at 60 mph (~50 J). [246] 10 28: 3.8×10 28 J: Kinetic energy of the Moon in its orbit around the Earth (counting only its velocity relative to the Earth) [247] [248] 7×10 28 J
The vibrations of a diatomic molecule are an example of a two-body version of the quantum harmonic oscillator. In this case, the angular frequency is given by ω = k μ {\displaystyle \omega ={\sqrt {\frac {k}{\mu }}}} where μ = m 1 m 2 m 1 + m 2 {\displaystyle \mu ={\frac {m_{1}m_{2}}{m_{1}+m_{2}}}} is the reduced mass and m 1 {\displaystyle ...