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In chemistry, a chemical oscillator is a complex mixture of reacting chemical compounds in which the concentration of one or more components exhibits periodic changes. They are a class of reactions that serve as an example of non-equilibrium thermodynamics with far-from-equilibrium behavior.
The period, the time for one complete oscillation, is given by the expression = =, which is a good approximation of the actual period when is small. Notice that in this approximation the period τ {\displaystyle \tau } is independent of the amplitude θ 0 {\displaystyle \theta _{0}} .
The equation for describing the period: = shows the period of oscillation is independent of the amplitude, though in practice the amplitude should be small. The above equation is also valid in the case when an additional constant force is being applied on the mass, i.e. the additional constant force cannot change the period of oscillation.
The time taken for an oscillation to occur is often referred to as the oscillatory period. The systems where the restoring force on a body is directly proportional to its displacement, such as the dynamics of the spring-mass system, are described mathematically by the simple harmonic oscillator and the regular periodic motion is known as simple ...
In practice N is set to 1 cycle and t = T = time period for 1 cycle, to obtain the more useful relation: = / Hz = s −1 [T] −1: Angular frequency/ pulsatance ω = = / Hz = s −1 [T] −1: Oscillatory velocity v, v t, v: Longitudinal waves:
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.
The period T is the time taken to complete one cycle of an oscillation or rotation. The frequency and the period are related by the equation [ 4 ] f = 1 T . {\displaystyle f={\frac {1}{T}}.} The term temporal frequency is used to emphasise that the frequency is characterised by the number of occurrences of a repeating event per unit time.
The oscillation frequency of the standing wave, multiplied by the Planck constant, is the energy of the state according to the Planck–Einstein relation. Stationary states are quantum states that are solutions to the time-independent Schrödinger equation : H ^ | Ψ = E Ψ | Ψ , {\displaystyle {\hat {H}}|\Psi \rangle =E_{\Psi }|\Psi \rangle ...
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