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Coupled spring equationsFay, TH, Graham, SD January 2003 (has links)
Coupled spring equations for modelling the motion of two springs with
weights attached, hung in series from the ceiling are described. For the linear
model using Hooke’s Law, the motion of each weight is described by a fourthorder
linear differential equation. A nonlinear model is also described and
damping and external forcing are considered. The model has many features that
permit the meaningful introduction of many concepts including: accuracy of
numerical algorithms, dependence on parameters and initial conditions, phase
and synchronization, periodicity, beats, linear and nonlinear resonance, limit
cycles, harmonic and subharmonic solutions. These solutions produce a wide
variety of interesting motions and the model is suitable for study as a computer
laboratory project in a beginning course on differential equations or as an
individual or a small-groupundergraduate research project.
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Coupled spring equationsFay, TH 01 January 2003 (has links)
Summary
Coupled spring equations for modelling the motion of two springs with
weights attached, hung in series from the ceiling are described. For the linear
model using Hooke’s Law, the motion of each weight is described by a fourthorder
linear differential equation. A nonlinear model is also described and
damping and external forcing are considered. The model has many features that
permit the meaningful introduction of many concepts including: accuracy of
numerical algorithms, dependence on parameters and initial conditions, phase
and synchronization, periodicity, beats, linear and nonlinear resonance, limit
cycles, harmonic and subharmonic solutions. These solutions produce a wide
variety of interesting motions and the model is suitable for study as a computer
laboratory project in a beginning course on differential equations or as an
individual or a small-groupundergraduate research project.
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Modelo pedagógico de resistores elétricos para descrever fraturas em sistemas físicos / Pedagogical model of electrical resistors describe fractures in physical systemsCunha, Airton Modesto da 09 August 2018 (has links)
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Previous issue date: 2018-08-09 / The present dissertation is the result of the educational, “Teaching model of electrical
resistors to describe fractures in physical systems”, product worked in a class of the third
year of high school of the State School Prof. Marcolino de Barros of the municipality of Patos
de Minas-MG. In which, we present a simple pedagogical model with the purpose of studying
the complex process of ruptures in physical systems. For this, we developed an experimental
model together with its theoretical counterpart where we consider a system of electric
resistors network subject to a potential difference and analyze the current that passes
through the system as a function of the random removal of their resistive components. We
use a circuit board, voltage source stabilized at a pre-established potential difference, and a
resistor network with a few ohms units each. After the proposed experiments are executed,
we obtained appropriate experimental data and from these graphs are generated with which
the dependence of the current through the circuit with the interruption of the joints is shown.
Taking into account that this system behaves as an ohmic system, the model is used to study
several relevant physical concepts. As is the case of an elastic solid subject to Hooke’s law-
like deformations, this is then a very broad model. / A presente dissertação é resultado de nosso produto educacional, “Modelo pedagógico de
resistores elétricos para descrever fraturas em sistemas físicos”, trabalhado em uma turma
do terceiro ano do ensino médio da Escola Estadual Prof. Marcolino de Barros do município
de Patos de Minas-MG. No qual, apresentamos um modelo pedagógico simples com a
finalidade de estudar o complexo processo de rupturas em sistemas físicos. Para tanto,
desenvolvemos um modelo experimental munido de sua contraparte teórica onde
consideramos um sistema de resistores elétricos sujeito a uma diferença de potencial e
analisamos a corrente que passa através do sistema em função da remoção aleatória doscomponentes resistivos. Usamos uma placa de circuitos, fonte de tensão estabilizada em uma
diferença de potencial pré -estabelecida e uma malha de resistores com algumas unidades de
ohms cada. Realizadas as experiências propostas obtivemos apropriados dados
experimentais e a partir destes foram gerados gráficos com os quais são mostrados a
dependência da corrente através do circuito com a interrupção das junções. Levando em
consideração que este sistema se comporta como um sistema ôhmico, o modelo é usado para
estudar vários conceitos físicos relevantes. Como é o caso de um solido elástico sujeito a
deformações do tipo lei de Hooke, sendo este então um modelo de caráter bem amplo.
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Žemės plutos horizantaliųjų judesių Ignalinos atominės elektrinės rajone tyrimas geodeziniais metodais / Research of the eartch’s crust horizontal movements in the Ignalina nuclear power plant region by geodetic methodsStanionis, Arminas 17 January 2006 (has links)
A method prepared and created algorithm for computations and evaluation of relation between Earth’s crust horizontal deformations and variations of tectonic stresses. Hooke’s law was used for relation description. Method of evaluation of Earth’s crust horizontal deformations was improved as well as modelling method based on observation data. Elements of deformation tensors were evaluated by applying finite element method. New data of Earth’s crust horizontal movements and their geodynamic interpretation at the Ignalina Nuclear Power Plant region were obtained.
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