Free Oscillations of a Damped Simple Pendulum: An Analog Simulation Experiment

2019 ◽  
Vol 01 (04) ◽  
pp. 1950015 ◽  
Author(s):  
Ivan Skhem Sawkmie ◽  
Mangal C. Mahato
Keyword(s):  
Harmonic Oscillator ◽  
Free Oscillation ◽  
Simulation Experiment ◽  
Free Oscillations ◽  
Analog Simulation ◽  
Simple Pendulum ◽  
Electronic Circuitry ◽  
Undergraduate Laboratory ◽  
Angular Amplitude ◽  
Theoretical Results

The frequency of free oscillation of a damped simple pendulum with large amplitude depends on its amplitude unlike the amplitude-independent frequency of oscillation of a damped simple harmonic oscillator. This aspect is not adequately emphasized in the undergraduate courses due to experimental and theoretical difficulties. We propose an analog simulation experiment to study the free oscillations of a simple pendulum that could be performed in an undergraduate laboratory. The needed sinusoidal potential is obtained approximately by using the available AD534 IC by suitably augmenting the electronic circuitry. To keep the circuit simple enough we restrict the initial angular amplitude of the simple pendulum to a maximum of [Formula: see text]. The results compare well qualitatively with the theoretical results. The small quantitative discrepancy is attributed to the inexact nature of the used “sinusoidal potential”.

scholarly journals Selecting a Model for Forecasting

Econometrics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 26
Author(s):  
Jennifer L. Castle ◽  
Jurgen A. Doornik ◽  
David F. Hendry
Keyword(s):  
Structural Breaks ◽  
Simulation Experiment ◽  
Structural Break ◽  
Static Model ◽  
Forecast Period ◽  
Forecast Performance ◽  
Significance Level ◽  
Forecasting Models ◽  
Theoretical Results

We investigate forecasting in models that condition on variables for which future values are unknown. We consider the role of the significance level because it guides the binary decisions whether to include or exclude variables. The analysis is extended by allowing for a structural break, either in the first forecast period or just before. Theoretical results are derived for a three-variable static model, but generalized to include dynamics and many more variables in the simulation experiment. The results show that the trade-off for selecting variables in forecasting models in a stationary world, namely that variables should be retained if their noncentralities exceed unity, still applies in settings with structural breaks. This provides support for model selection at looser than conventional settings, albeit with many additional features explaining the forecast performance, and with the caveat that retaining irrelevant variables that are subject to location shifts can worsen forecast performance.

Free oscillation observations through 1968

1969 ◽  
Vol 59 (5) ◽  
pp. 2079-2099
Author(s):  
John S. Derr
Keyword(s):  
Confidence Level ◽  
Free Oscillation ◽  
Statistical Tests ◽  
Standard Errors ◽  
Free Oscillations ◽  
The Earth ◽  
Earth Models ◽  
Earth Structures ◽  
Path Dependent ◽  
Consistent Basis

abstract All observations of the free oscillations of the Earth published through 1968 are weighted to produce a set of means and standard errors of the means. Fundamental orders 0 to 97 for spheroidal and 2 to 99 for torsional are treated, as well as many overtones up to order 49. Statistical tests indicate that some observations are path dependent at the 99 per cent confidence level. Comparison of these means and standard errors with published Earth models indicate that they form a consistent basis for inversion of free oscillation observations to infer Earth structures.

scholarly journals A Vibration-Isolated Body of Chaotic Prediction

2011 ◽  
Vol 2-3 ◽  
pp. 978-983
Author(s):  
Yong Yi Gao ◽  
Shi Ping Zhan ◽  
Ban Gyan Li
Keyword(s):  
High Frequency ◽  
Simulation Experiment ◽  
Variable Parameter ◽  
Slow Variable ◽  
State Equation ◽  
Analytical Prediction ◽  
Vibration Isolator ◽  
Weak Nonlinearity ◽  
Analog Simulation ◽  
Inherent Frequency

The nonlinear dynamics equation of passive vibration isolator is established in this paper. According to the nonlinear vibration theory, the average equation of slow-varying primary harmonic in the condition of weak nonlinearity is abstained , and derived a discrete mapping of the harmonic slow variable parameter state equation, then get the analytical conditions of chaos in the passive vibration isolator, the analytical results show that only when the vibration frequency of the groundsill is higher than the inherent frequency of the passive vibration isolator, the chaos can be observed, when the groundsill vibrate with the large amplitude and high frequency vibration, the chaos can’t be observed in the passive vibration isolator system. Finally the analytical prediction is validated by analog simulation experiment, and gets the conclusion that the prediction matches well with the simulation results.

HOMOCLINIC BIFURCATION AND CHAOS IN COUPLED SIMPLE PENDULUM AND HARMONIC OSCILLATOR UNDER BOUNDED NOISE EXCITATION

2005 ◽  
Vol 15 (01) ◽  
pp. 233-243 ◽  
Author(s):  
W. Q. ZHU ◽  
Z. H. LIU
Keyword(s):  
Harmonic Oscillator ◽  
Random Motion ◽  
Homoclinic Bifurcation ◽  
Mean Square ◽  
Bounded Noise ◽  
Bifurcation And Chaos ◽  
Simple Pendulum ◽  
Onset Of Chaos ◽  
Weakly Coupled ◽  
Threshold Amplitude

The homoclinic bifurcation and chaos in a system of weakly coupled simple pendulum and harmonic oscillator subject to light dampings and weakly external and (or) parametric excitation of bounded noise is studied. The random Melnikov process is derived and mean-square criteria is used to determine the threshold amplitude of the bounded noise for the onset of chaos in the system. The threshold amplitude is also determined by vanishing the numerically calculated maximal Lyapunov exponent. The threshold amplitudes are further confirmed by using the Poincaré maps, which indicate the path from periodic motion to chaos or from random motion to random chaos in the system as the amplitude of bounded noise increases.

scholarly journals Split free oscillation amplitudes for the 1960 Chilean and 1964 Alaskan earthquakes

1977 ◽  
Vol 67 (3) ◽  
pp. 651-660 ◽  
Author(s):  
Robert J. Geller ◽  
Seth Stein
Keyword(s):  
Surface Waves ◽  
Volume Change ◽  
Free Oscillation ◽  
Additional Data ◽  
Normal Modes ◽  
Source Mechanisms ◽  
Split Mode ◽  
Theoretical Results

abstract Splitting of the Earth's normal modes was observed for both the 1960 Chilean and 1964 Alaskan earthquakes. The strong peaks in the observed spectrum of each split multiplet correspond to singlets with much higher amplitudes than the others. Using theoretical results we have derived elsewhere (Stein and Geller, 1977a), we are able to predict this pattern. We show that the source mechanisms inferred for these earthquakes from surface waves are consistent with the observed pattern of relative spectral amplitudes of the split modes. However other mechanisms, such as a slow isotropic volume change, are also consistent with the split-mode amplitudes and are excluded only by additional data.

Small oscillations of systems with one degree of freedom

2020 ◽  
pp. 175-190
Author(s):  
Gleb L. Kotkin ◽  
Valeriy G. Serbo
Keyword(s):  
Differential Cross Section ◽  
Potential Energy ◽  
Harmonic Oscillator ◽  
Cross Section ◽  
Differential Cross ◽  
Travelling Wave ◽  
Fast Particle ◽  
Free Oscillations ◽  
Periodic Force ◽  
Small Oscillations

This chapter addresses the small free oscillations for particle moving near the minimum of the potential energy, an oscillator with friction under action of a given force, and the stable oscillations of an oscillator which is acted upon by a periodic force. The authors also discuss the differential cross section for the oscillator which excited to an given energy by a fast particle and a harmonic oscillator in the field of the travelling wave.

Small oscillations of systems with one degree of freedom

2020 ◽  
pp. 25-28
Author(s):  
Gleb L. Kotkin ◽  
Valeriy G. Serbo
Keyword(s):  
Differential Cross Section ◽  
Potential Energy ◽  
Harmonic Oscillator ◽  
Cross Section ◽  
Differential Cross ◽  
Travelling Wave ◽  
Fast Particle ◽  
Free Oscillations ◽  
Periodic Force ◽  
Small Oscillations

This chapter addresses the small free oscillations for particle moving near the minimum of the potential energy, an oscillator with friction under action of a given force, and the stable oscillations of an oscillator which is acted upon by a periodic force. The authors also discuss the differential cross section for the oscillator which excited to an given energy by a fast particle and a harmonic oscillator in the field of the travelling wave.

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