Search results
Results From The WOW.Com Content Network
A simple harmonic oscillator is an oscillator that is neither driven nor damped.It consists of a mass m, which experiences a single force F, which pulls the mass in the direction of the point x = 0 and depends only on the position x of the mass and a constant k.
The quantum harmonic oscillator is the quantum-mechanical analog of the classical harmonic oscillator. Because an arbitrary smooth potential can usually be approximated as a harmonic potential at the vicinity of a stable equilibrium point , it is one of the most important model systems in quantum mechanics.
The equation is given by ¨ + ˙ + + = (), where the (unknown) function = is the displacement at time t, ˙ is the first derivative of with respect to time, i.e. velocity, and ¨ is the second time-derivative of , i.e. acceleration.
The damping ratio is a parameter, usually denoted by ζ (Greek letter zeta), [7] that characterizes the frequency response of a second-order ordinary differential equation. It is particularly important in the study of control theory. It is also important in the harmonic oscillator. In general, systems with higher damping ratios (one or greater ...
This plot corresponds to solutions of the complete Langevin equation for a lightly damped harmonic oscillator, obtained using the Euler–Maruyama method. The left panel shows the time evolution of the phase portrait at different temperatures. The right panel captures the corresponding equilibrium probability distributions.
Velocity (blue line) and particle excursion (red dots) as a function of the distance to the wall. In fluid dynamics, Stokes problem also known as Stokes second problem or sometimes referred to as Stokes boundary layer or Oscillating boundary layer is a problem of determining the flow created by an oscillating solid surface, named after Sir ...
The Q factor is a parameter that describes the resonance behavior of an underdamped harmonic oscillator (resonator). Sinusoidally driven resonators having higher Q factors resonate with greater amplitudes (at the resonant frequency) but have a smaller range of frequencies around that frequency for which they resonate; the range of frequencies for which the oscillator resonates is called the ...
Relaxation oscillation in the Van der Pol oscillator without external forcing. The nonlinear damping parameter is equal to μ = 5. [12] When μ = 0, i.e. there is no damping function, the equation becomes + = This is a form of the simple harmonic oscillator, and there is always conservation of energy.