The equation of motion of the classic anharmonic oscillator is shown to have an exact solution in terms of elliptic functions both in the absence and in the presence of a sufficient weak external force. An external force depending on time as an elliptic function gives rise to resonance as in...
The quantum damped harmonic oscillator Chung-InUm, ...Thomas F.George, inPhysics Reports, 2002 Theequation of motioncan be expressed in the conventionalcommutatorform, and thus the general functionsF+(z†,z̃†)andF−(z,z̃)can be written as sums of the factorizing termsF+F−give...
An elementary method, based on the use of complex variables, is proposed for solving the equation of motion of a simple harmonic oscillator. The method is first applied to the equation of motion for an undamped oscillator and it is then extended to the more important case of a damped ...
Simple harmonic motion (SHM) is a special case of periodic motion, where the only force is a restorative force and the motion is a simple oscillation. One of the basic properties of SHM is that the restoring force is directly proportional to the displacement from the equilibrium position. Retu...
The simplest relativistic field theory is described by the Klein-Gordon equation of motion for a scalar field ##\large \phi(\vec{x},t)##: $$\large \frac{\partial^2\phi}{\partial t^2}-\nabla^2\phi+m^2\phi=0.$$ We... jcap Thread Aug 21, 2018 Tags Antiparticles Energy Field...
This paper presents an investigation into the non-linear behaviour of an impact oscillator with the addition of dry friction. The equations that govern the... KM Cone,RI Zadoks - 《Journal of Sound & Vibration》 被引量: 102发表: 1995年 Numerical integration of the equation of motion of an...
Simple harmonic motion depends on the stiffness of the restoring force and the mass of the object. A simple harmonic oscillator with large mass oscillates with less frequency. Theoscillatorwith high restoring force oscillates with high frequency. The displacement, velocity, amplitude and force parameter...
To begin, recall that SHM is characterized by the equation of motion given asF = -kx. This corresponds to the potentialV = ½kx2. The value of the proportionality constant is given byk = mw2. This gives us all the tools we need to set up the Schrödinger equation. ...
The equations of motion for observables strongly depend on the deformation function. The expectation values of the number operator and squared number operator are calculated in the limit of a small deformation parameter for the case of zero temperature of the thermal bath. The steady state solution...
Classical and quantum mechanics of the damped harmonic oscillator The relations between various treatments of the classical linearly damped harmonic oscillator and its quantization are investigated. In the course of a his... H Dekker - 《Physics Reports》...