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It is shown that the classical damped harmonic oscillator belongs to the family of fourth-order Pais-Uhlenbeck oscillators. It follows that the solutions to the damped harmonic oscillator equation make the Pais-Uhlenbeck action stationary. Two systematic approaches are given for deriving the Pais-Uhlenbeck action from the damped harmonic oscillator equation, and it may be possible to use these methods to identify stationary action principles for other dissipative systems which do not conform to Hamiltons principle. It is also shown that for every damped harmonic oscillator $x$, there exists a two-parameter family of dual oscillators $y$ satisfying the Pais-Uhlenbeck equation. The damped harmonic oscillator and any of its duals can be interpreted as a system of two coupled oscillators with atypical spring stiffnesses (not necessarily positive and real-valued). For overdamped systems, the resulting coupled oscillators should be physically achievable and may have engineering applications. Finally, a new physical interpretation is given for the optimal damping ratio $zeta=1/sqrt{2}$ in control theory.
We return to the description of the damped harmonic oscillator by means of a closed quantum theory with a general assessment of previous works, in particular the Bateman-Caldirola-Kanai model and a new model recently proposed by one of the authors. W
A system obeying the harmonic oscillator equation of motion can be used as a force or proper acceleration sensor. In this short review we derive analytical expressions for the sensitivity of such sensors in a range of different situations, considerin
Time evolution of a harmonic oscillator linearly coupled to a heat bath is compared for three classes of initial states for the bath modes - grand canonical ensemble, number states and coherent states. It is shown that for a wide class of number stat
An approximate solution is presented for simple harmonic motion in the presence of damping by a force which is a general power-law function of the velocity. The approximation is shown to be quite robust, allowing for a simple way to investigate ampli
The status of classical stability in higher-derivative systems is still subject to discussions. In this note, we argue that, contrary to general belief, many higher-derivative systems are classically stable. The main tool to see this property are Nek