Response of a harmonic oscillator to a resonance frequency step

2004 ◽  
pp. 223-224 ◽  
Author(s):  
Thomas Ihn
Keyword(s):  
Harmonic Oscillator ◽  
Resonance Frequency

Analytical expressions for real and complex Fano parameters in a simple classical harmonic oscillator system

2021 ◽  
Author(s):  
Seiji MIZUNO
Keyword(s):  
Harmonic Oscillator ◽  
Resonance Frequency ◽  
Real Number ◽  
Wave Phenomenon ◽  
Fano Resonance ◽  
Equation Of Motion ◽  
Coupled Oscillator ◽  
Physical Systems ◽  
Oscillator System ◽  
Analytical Expressions

Abstract We analytically study the Fano resonance in a simple coupled oscillator system. We demonstrate directly from the equation of motion that the resonance profile observed in this system is generally described by the Fano formula with a complex Fano parameter. The analytical expressions are derived for the resonance frequency, resonance width, and Fano parameter, and the conditions under which the Fano parameter becomes a real number are examined. These expressions for the simple system are also expected to be helpful for considering various other physical systems because the Fano resonance is a general wave phenomenon.

scholarly journals Fundamental limits and optimal estimation of the resonance frequency of a linear harmonic oscillator

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Mingkang Wang ◽  
Rui Zhang ◽  
Robert Ilic ◽  
Yuxiang Liu ◽  
Vladimir A. Aksyuk
Keyword(s):  
Harmonic Oscillator ◽  
Resonance Frequency ◽  
Estimation Method ◽  
Optimal Estimation ◽  
Frequency Measurement ◽  
Thermal Fluctuations ◽  
Fundamental Limits ◽  
Linear Harmonic Oscillator ◽  
High Bandwidth ◽  
Frequency Estimator

AbstractAll physical oscillators are subject to thermodynamic and quantum perturbations, fundamentally limiting measurement of their resonance frequency. Analyses assuming specific ways of estimating frequency can underestimate the available precision and overlook unconventional measurement regimes. Here we derive a general, estimation-method-independent Cramer Rao lower bound for a linear harmonic oscillator resonance frequency measurement uncertainty, seamlessly accounting for the quantum, thermodynamic and instrumental limitations, including Fisher information from quantum backaction- and thermodynamically driven fluctuations. We provide a universal and practical maximum-likelihood frequency estimator reaching the predicted limits in all regimes, and experimentally validate it on a thermodynamically limited nanomechanical oscillator. Low relative frequency uncertainty is obtained for both very high bandwidth measurements (≈10−5 for τ = 30 μs) and measurements using thermal fluctuations alone (<10−6). Beyond nanomechanics, these results advance frequency-based metrology across physical domains.

Actuation and dynamic mechanical characteristics of a core free flat dielectric electro-active polymer soft actuator

2020 ◽  
Vol 14 (4) ◽  
pp. 7396-7404
Author(s):  
Abdul Malek Abdul Wahab ◽  
Emiliano Rustighi ◽  
Zainudin A.
Keyword(s):  
Theoretical Model ◽  
Resonance Frequency ◽  
Dynamic Testing ◽  
Experimental Results ◽  
Percentage Error ◽  
Initial Tension ◽  
Average Percentage ◽  
Soft Actuator ◽  
Average Percentage Error ◽  
Mechanical Dynamics

Various complex shapes of dielectric electro-active polymer (DEAP) actuator have been promoted for several types of applications. In this study, the actuation and mechanical dynamics characteristics of a new core free flat DEAP soft actuator were investigated. This actuator was developed by Danfoss PolyPower. DC voltage of up to 2000 V was supplied for identifying the actuation characteristics of the actuator and compare with the existing formula. The operational frequency of the actuator was determined by dynamic testing. Then, the soft actuator has been modelled as a uniform bar rigidly fixed at one end and attached to mass at another end. Results from the theoretical model were compared with the experimental results. It was found that the deformation of the current actuator was quadratic proportional to the voltage supplied. It was found that experimental results and theory were not in good agreement for low and high voltage with average percentage error are 104% and 20.7%, respectively. The resonance frequency of the actuator was near 14 Hz. Mass of load added, inhomogeneity and initial tension significantly affected the resonance frequency of the soft actuator. The experimental results were consistent with the theoretical model at zero load. However, due to inhomogeneity, the frequency response function’s plot underlines a poor prediction where the theoretical calculation was far from experimental results as values of load increasing with the average percentage error 15.7%. Hence, it shows the proposed analytical procedure not suitable to provide accurate natural frequency for the DEAP soft actuator.

Influence of Bone Quality, Drilling Protocol, Implant Diameter/Length on Primary Stability: An In Vitro Comparative Study on Insertion Torque and Resonance Frequency Analysis

2020 ◽  
Vol 46 (3) ◽  
pp. 182-189 ◽  
Author(s):  
Davide Farronato ◽  
Mattia Manfredini ◽  
Michele Stocchero ◽  
Mattia Caccia ◽  
Lorenzo Azzi ◽  
...  
Keyword(s):  
Resonance Frequency ◽  
Bone Quality ◽  
Frequency Analysis ◽  
Primary Stability ◽  
Mean Difference ◽  
Insertion Torque ◽  
Resonance Frequency Analysis ◽  
Bone Response ◽  
Implant Length

The aim of this study was to evaluate the influence of bone quality, drilling technique, implant diameter, and implant length on insertion torque (IT) and resonance frequency analysis (RFA) of a prototype-tapered implant with knife-edge threads. The investigators hypothesized that IT would be affected by variations in bone quality and drilling protocol, whereas RFA would be less influenced by such variables. The investigators implemented an in vitro experiment in which a prototype implant was inserted with different testing conditions into rigid polyurethane foam blocks. The independent variables were: bone quality, drilling protocol, implant diameter, and implant length. Group A implants were inserted with a conventional drilling protocol, whereas Group B implants were inserted with an undersized drilling protocol. Values of IT and RFA were measured at implant installation. IT and RFA values were significantly correlated (Pearson correlation coefficient: 0.54). A multivariable analysis showed a strong model. Higher IT values were associated with drilling protocol B vs A (mean difference: 71.7 Ncm), implant length (3.6 Ncm increase per mm in length), and substrate density (0.199 Ncm increase per mg/cm3 in density). Higher RFA values were associated with drilling protocol B vs A (mean difference: 3.9), implant length (1.0 increase per mm in length), and substrate density (0.032 increase per mg/cm3 in density). Implant diameter was not associated with RFA or IT. Within the limitations of an in vitro study, the results of this study suggest that the studied implant can achieve good level of primary stability in terms of IT and RFA. A strong correlation was found between values of IT and RFA. Both parameters are influenced by the drilling protocol, implant length, and substrate density. Further studies are required to investigate the clinical response in primary stability and marginal bone response.

PECULIARITIES OF THE RESONANCE FREQUENCY MECHANICAL TUNING OF THE WAVEGUIDE-DIELECTRIC RESONATOR

2013 ◽  
Vol 72 (19) ◽  
pp. 1739-1746
Author(s):  
R. I. Belous ◽  
S. P. Martynyuk ◽  
A. P. Motornenko ◽  
I. G. Skuratovskiy ◽  
O. I. Khazov
Keyword(s):  
Resonance Frequency ◽  
Dielectric Resonator ◽  
Mechanical Tuning

Rosen-Chambers Variation Theory of Linearly-Damped Classic and Quantum Oscillator

2014 ◽  
Vol 4 (1) ◽  
pp. 404-426
Author(s):  
Vincze Gy. Szasz A.
Keyword(s):  
Harmonic Oscillator ◽  
Classical Mechanics ◽  
Universal Time ◽  
Variation Theory ◽  
Quantum Oscillator ◽  
Variation Principle ◽  
Poisson Brackets ◽  
Mathematical Meaning ◽  
Damped Harmonic Oscillator ◽  
Damped Oscillator

Phenomena of damped harmonic oscillator is important in the description of the elementary dissipative processes of linear responses in our physical world. Its classical description is clear and understood, however it is not so in the quantum physics, where it also has a basic role. Starting from the Rosen-Chambers restricted variation principle a Hamilton like variation approach to the damped harmonic oscillator will be given. The usual formalisms of classical mechanics, as Lagrangian, Hamiltonian, Poisson brackets, will be covered too. We shall introduce two Poisson brackets. The first one has only mathematical meaning and for the second, the so-called constitutive Poisson brackets, a physical interpretation will be presented. We shall show that only the fundamental constitutive Poisson brackets are not invariant throughout the motion of the damped oscillator, but these show a kind of universal time dependence in the universal time scale of the damped oscillator. The quantum mechanical Poisson brackets and commutation relations belonging to these fundamental time dependent classical brackets will be described. Our objective in this work is giving clearer view to the challenge of the dissipative quantum oscillator.

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