This section collects and defines all the data needed to build the instance models.
| 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 | |
| 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 | |
| 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, DD:periodSHMDD, and GD:angFrequencyGD |
| 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 | |
| Source | – |
| RefBy | GD:periodPend |
| 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 | |
| Source | – |
| RefBy | GD:periodPend and DD:angFrequencyDD |