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Simple Pendulum Model

Source Notebook

Model of a simple pendulum

Examples

Basic Examples (2) 

Retrieve the model:

In[1]:=
ResourceData[\!\(\* TagBox["\"\<Simple Pendulum Model\>\"", #& , BoxID -> "ResourceTag-Simple Pendulum Model-Input", AutoDelete->True]\)]
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The icon:

In[2]:=
ResourceData[\!\(\* TagBox["\"\<Simple Pendulum Model\>\"", #& , BoxID -> "ResourceTag-Simple Pendulum Model-Input", AutoDelete->True]\), "Icon"]
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Scope & Additional Elements (4) 

Available content elements:

In[3]:=
\!\(\* TagBox[ RowBox[{"ResourceObject", "[", "\"\<Simple Pendulum Model\>\"", "]"}], #& , BoxID -> "ResourceTag-Simple Pendulum Model-Input", AutoDelete->True]\)["ContentElements"]
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The available model types:

In[4]:=
ResourceData[\!\(\* TagBox["\"\<Simple Pendulum Model\>\"", #& , BoxID -> "ResourceTag-Simple Pendulum Model-Input", AutoDelete->True]\), "AvailableModelTypes"]
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The operating point:

In[5]:=
ResourceData[\!\(\* TagBox["\"\<Simple Pendulum Model\>\"", #& , BoxID -> "ResourceTag-Simple Pendulum Model-Input", AutoDelete->True]\), "OperatingPoint"]
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The parameters:

In[6]:=
ResourceData[\!\(\* TagBox["\"\<Simple Pendulum Model\>\"", #& , BoxID -> "ResourceTag-Simple Pendulum Model-Input", AutoDelete->True]\), "Parameters"]
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Analysis (3) 

The linear models about the two equilibrium positions for the set of parameter values:
In[7]:=
{ssm0, ssm180} = Table[ResourceData[\!\(\* TagBox["\"\<Simple Pendulum Model\>\"", #& , BoxID -> "ResourceTag-Simple Pendulum Model-Input", AutoDelete->True]\), "StateSpaceModel"] /. {\[CapitalTheta] -> ang}, {ang, {0, \[Pi]}}] /. ResourceData[\!\(\* TagBox["\"\<Simple Pendulum Model\>\"", #& , BoxID -> "ResourceTag-Simple Pendulum Model-Input", AutoDelete->True]\), "Parameters"]
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The response of the model linearized around 0 is stable, while the one around 180° is unstable:
In[8]:=
Grid[{Table[ Plot[Evaluate@ OutputResponse[{sys, {179 °, 0}}, {0}, {t, 0, 20}], {t, 0, 20}, PlotRange -> All], {sys, {ssm0, ssm180}}]}, Spacings -> 2]
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The affine model shows the pendulum reaching the stable equilibrium position from the unstable position:

In[9]:=
OutputResponse[{ResourceData[\!\(\* TagBox["\"\<Simple Pendulum Model\>\"", #& , BoxID -> "ResourceTag-Simple Pendulum Model-Input", AutoDelete->True]\)] /. \[CapitalTheta] -> \[Pi] /. ResourceData[\!\(\* TagBox["\"\<Simple Pendulum Model\>\"", #& , BoxID -> "ResourceTag-Simple Pendulum Model-Input", AutoDelete->True]\), "Parameters"], {179 °, 0}}, {0}, {t, 0, 20}]; Plot[%, {t, 0, 20}, PlotRange -> All]
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Suba Thomas, "Simple Pendulum Model" from the Wolfram Data Repository (2025)  

Data Resource History

  • Date Created:

Publisher Information

  • Prepared for the Wolfram Data Repository By: Maher Kuzbari, Suba Thomas
  • Publisher of Record: Suba Thomas