The simplest example is once more the damped harmonic oscillator.

Mathematically, it can be modeled as a damped harmonic oscillator.

Given the equation for the damped harmonic oscillator:

A damped harmonic oscillator can be:

For instance, consider a damped harmonic oscillator such as a pendulum, or a resonant L-C tank circuit.

The transient solutions are the same as the unforced () damped harmonic oscillator and represent the systems response to other events that occurred previously.

We quantize the system of a damped harmonic oscillator coupled to its time-reversed image, known as Bateman's dual system.

If the polymer is treated as a classical damped harmonic oscillator, both the elastic modulus and the damping characteristics can be obtained.

For interest's sake, this ODE has a physical interpretation as a driven damped harmonic oscillator; y represents the steady state, and is the transient.

A constant of the motion, in addition to what exists in the literature, is presented for the damped harmonic oscillator and its dynamical origin is investigated.

Under a new quantization scheme, the exact wave functions of the time-dependent driven damped harmonic oscillator with time-dependent mass and frequency are obtained.

We calculate the thermal correlation functions of the one-dimensional damped harmonic oscillator in contact with a reservoir, in an exact form by applying Green's function method.

Values of Ep(q) and G(q) obtained by fitting the energy spectra at 20 K to the damped harmonic oscillator scattering function.

In the classical approach, the Rabi problem can be represented by the solution to the driven, damped harmonic oscillator with the electric part of the Lorentz force as the driving term:

The coherent states for the damped harmonic oscillator and variable mass or frequency harmonic oscillator are the special cases of the coherent states for the system studied in this paper.

We apply results on symmetries of equations of motion and equivalent Lagrangians to obtain a constant of motion for a particle travelling through a viscous medium and for the damped harmonic oscillator.

In DMTA a sinusoidal stress is applied to the polymer, and based on the polymer's deformation the elastic modulus and damping characteristics are obtained (assuming the polymer is a damped harmonic oscillator).

For a damped harmonic oscillator with mass m, damping coefficient c, and spring constant k, it can be defined as the ratio of the damping coefficient in the system's differential equation to the critical damping coefficient: