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Data Definitions

This section collects and defines all the data needed to build the instance models.

$x$ -component of initial position

Refname	DD:positionIX
Label	$x$ -component of initial position
Symbol	${{p_{\text{x}}}^{\text{i}}}$
Units	${\text{m}}$
Equation	${{p_{\text{x}}}^{\text{i}}}={L_{\text{rod}}}\,\sin\left({θ_{i}}\right)$
Description	${{p_{\text{x}}}^{\text{i}}}$ is the $x$ -component of initial position ( ${\text{m}}$ ) ${L_{\text{rod}}}$ is the length of the rod ( ${\text{m}}$ ) ${θ_{i}}$ is the initial pendulum angle ( ${\text{rad}}$ )
Notes	${{p_{\text{x}}}^{\text{i}}}$ is the horizontal position ${{p_{\text{x}}}^{\text{i}}}$ is shown in Fig:sglpend.
Source	–
RefBy

$y$ -component of initial position

Refname	DD:positionIY
Label	$y$ -component of initial position
Symbol	${{p_{\text{y}}}^{\text{i}}}$
Units	${\text{m}}$
Equation	${{p_{\text{y}}}^{\text{i}}}=-{L_{\text{rod}}}\,\cos\left({θ_{i}}\right)$
Description	${{p_{\text{y}}}^{\text{i}}}$ is the $y$ -component of initial position ( ${\text{m}}$ ) ${L_{\text{rod}}}$ is the length of the rod ( ${\text{m}}$ ) ${θ_{i}}$ is the initial pendulum angle ( ${\text{rad}}$ )
Notes	${{p_{\text{y}}}^{\text{i}}}$ is the vertical position ${{p_{\text{y}}}^{\text{i}}}$ is shown in Fig:sglpend.
Source	–
RefBy

Frequency

Refname	DD:frequencyDD
Label	Frequency
Symbol	$f$
Units	${\text{Hz}}$
Equation	$f=\frac{1}{T}$
Description	$f$ is the frequency ( ${\text{Hz}}$ ) $T$ is the period ( ${\text{s}}$ )
Notes	$f$ is the number of back and forth swings in one second
Source	–
RefBy	GD:periodPend, GD:angFrequencyGD, and DD:periodSHMDD

Angular frequency

Refname	DD:angFrequencyDD
Label	Angular frequency
Symbol	$Ω$
Units	${\text{s}}$
Equation	$Ω=\frac{2\,π}{T}$
Description	$Ω$ is the angular frequency ( ${\text{s}}$ ) $π$ is the ratio of circumference to diameter for any circle (Unitless) $T$ is the period ( ${\text{s}}$ )
Notes	$T$ is from DD:periodSHMDD
Source	–
RefBy	GD:periodPend

Period

Refname	DD:periodSHMDD
Label	Period
Symbol	$T$
Units	${\text{s}}$
Equation	$T=\frac{1}{f}$
Description	$T$ is the period ( ${\text{s}}$ ) $f$ is the frequency ( ${\text{Hz}}$ )
Notes	$T$ is from DD:frequencyDD
Source	–
RefBy	GD:periodPend and DD:angFrequencyDD