Using Manipulate with ListLinePlot data

Questions
1

I am attempting to plot a frequency amplitude response for a simple Duffing Problem. I have a range defined for gamma. This means that a, the amplitude is known. The sigma is the frequency of the system. Sigma is a function of the amplitude and gamma. Since gamma is defined as a range the amplitude is known and thus we can find sigma. I plotted the amplitude vs the frequency. I now want to wrap the plot with manipulate so that i can vary the magnitude of the force F, damping parameter c, and the non linearity mue. This is the code i have so far. This plot generates with the slide bars. When i press play however the plot remains static. Please help. Thank You.

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\[Omega] = 3.15;
\[Gamma] = Range[0.001, 3.1415, 0.001];
c = 0.01;
F = 0.1;
\[Mu] = 5;


a = (F*Sin[\[Gamma]])/(2*c*\[Omega]);
\[Sigma] = (3*\[Mu]*a^2)/(8*\[Omega]) - (F*Cos[\[Gamma]])/(
   2*a*\[Omega]);
data = Transpose@{\[Sigma], a};
Manipulate[
 ListLinePlot[data, PlotRange -> {{-1, 1}, {0, 1}}, 
  AxesLabel -> {sigma, amplitude}, 
  PlotLabel -> "MMS Duffing Frequency Response"], {{\[Mu], 1, 
   "Nonlinearity"}, 1, 5}, {{F, 0.1, "Force"}, 0.1, 
  1}, {{c, 0.01, "Damping"}, 0.01, 1}]
2

Please make sure you know the guidelines: https://wolfr.am/READ-1ST

Do NOT post code as images.

Please EDIT your post, copy-paste and properly format your code as explained in the guidelines.

3

The below is a MMA cell code copied into this post. Marking whats been pasted, then Ctrl+K (Windows). Copy back to a notebook of your own, and try it out.

Manipulate[
 	(* Preliminaries *)
 	a = (F*Sin[\[Gamma]])/(2*c*\[Omega]);
 	\[Sigma] = (3*\[Mu]*a^2)/(8*\[Omega]) - (F*Cos[\[Gamma]])/(2*a*\[Omega]);
 	data = Transpose@{\[Sigma], a};
 	(* Output *)
 	ListLinePlot[data,
  		PlotRange -> {{-1, 1}, {0, 1}},
  		AxesLabel -> {sigma, amplitude},
  		PlotLabel -> "MMS Duffing frequency Response"
  	],
 	(* Active controls *)
 	{{\[Mu], 1, "Nonlienarity"}, 1, 5},
 	{{F, 0.1, "Force"}, 0.1, 1},
 	{{c, 0.01, "Damping"}, 0.01, 1},
 	(* Local variables as controls *)
 	{\[Omega], 3.15, ControlType -> None},
 	{{\[Gamma], Range[0.001, 3.1415, 0.001]}, ControlType -> None},
 	{a, ControlType -> None},
 	{\[Sigma], ControlType -> None},
 	{data, ControlType -> None}
 ]
4

This one is a bit more efficient

\[Omega] = 3.15;
\[Gamma] = Range[0.001, 3.1415, 0.001];

Manipulate[
 	(* Preliminaries *)
 	a = (F*Sin[\[Gamma]])/(2*c*\[Omega]);
 	\[Sigma] = (3*\[Mu]*a^2)/(8*\[Omega]) - (F*Cos[\[Gamma]])/(2*a*\[Omega]);
 	data = Transpose@{\[Sigma], a};
 	(* Output *)
 	ListLinePlot[data,
  		PlotRange -> {{-1, 1}, {0, 1}},
  		AxesLabel -> {sigma, amplitude},
  		PlotLabel -> "MMS Duffing frequency Response"
  	],
 	(* Active controls *)
 	{{\[Mu], 1, "Nonlienarity"}, 1, 5},
 	{{F, 0.1, "Force"}, 0.1, 1},
 	{{c, 0.01, "Damping"}, 0.01, 1},
 	(* Local variables as controls *)
 	{a, ControlType -> None},
 	{\[Sigma], ControlType -> None},
 	{data, ControlType -> None},
 	(* Manipulate option *)
 	TrackedSymbols :> {\[Mu], F, c}
 ]