# Using Manipulate with ListLinePlot data

GROUPS:
 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. \[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}] 
 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} ] 
 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} ]