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[Model Hierarchy]

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The root page Model Hierarchy could not be found in space Modeling Applied to Problem Solving.
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Description and Assumptions

Problem Cues

Any object that experiences a linear restoring force or torque so that the equation of motion takes the form

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\begin

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[ a = \frac{d^{x}}{dt^{2}} = - \omega^

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x ]\end

or

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\begin

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[ \alpha = \frac{d^

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\theta}{dt^{2}} = -\omega^

x] \end

will experience simple harmonic motion with angular frequency ω. The prototypical example is an object of mass m attached to a spring with force constant k, in which case, by [Hooke's Law]:

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\begin

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[ a = -\frac

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]\end

giving simple harmonic motion with angular frequency $\sqrt{\dfrac

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{m}}$.


Page Contents


Prerequisite Knowledge

Prior Models

Vocabulary and Procedures


System

Constituents

A single point particle (or a system treated as a point particle with position specified by the center of mass).

State Variables

Time (t), position (x) , and velocity (v).


Interactions

Relevant Types

Some time-varying external influence that is confined to one dimension.

Interaction Variables

Acceleration (a(t)).


Model

Laws of Change

Differential Forms:

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\begin

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[ \frac

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= a]\end



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\begin

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[ \frac

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= v]\end



Integral Forms:

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\begin

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[ v(t) = v(t_

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)+\int_{t_{0}}^

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a\;dt]\end



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\begin

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[ x(t) = x(t_

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)+\int_{t_{0}}^

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v\;dt]\end



Diagrammatical Representations

  • Acceleration versus time graph.
  • Velocity versus time graph.
  • Position versus time graph.

Relevant Examples

None yet.


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RELATE wiki by David E. Pritchard is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 United States License.

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