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Labelling each curve and changing grid in ParametricPlot

• To: mathgroup at smc.vnet.net
• Subject: [mg129649] Labelling each curve and changing grid in ParametricPlot
• From: "Eduardo M. A. M. Mendes" <emammendes at gmail.com>
• Date: Sat, 2 Feb 2013 01:18:07 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• Delivered-to: l-mathgroup@wolfram.com
• Delivered-to: mathgroup-newout@smc.vnet.net
• Delivered-to: mathgroup-newsend@smc.vnet.net

Hello

I wonder whether someone out there could help me with the following problem.

plot[\[Tau]_, \[CapitalOmega]_] := Module[{arg, abs},
   {arg, abs} = Factor[Together[ComplexExpand[
        Through[{Arg, Abs}[(1 + I*2*\[CapitalOmega])/(1 + I*2*\[Tau]*\[CapitalOmega])]]]]];
    {arg/Degree, 20*Log10[abs]}]

ParametricPlot[Table[plot[\[Tau], \[CapitalOmega]], {\[Tau], {7, 8, 9, 10, 11, 12, 13, 14, 15}}],
  {\[CapitalOmega], -0.5, -0.01}, AspectRatio -> 1, GridLines -> Automatic,
  GridLinesStyle -> Dashed, ImageSize -> Large]

I need to label each curve with the value of tau and, instead of the normal grid, a grid based on the values of Omega.  

I saw something related to the label problem on the net but could not figure out how to change it to my case.   Something with Epilog.

Many thanks

Ed

• Follow-Ups:
  • Re: Labelling each curve and changing grid in ParametricPlot
    • From: Bob Hanlon <hanlonr357@gmail.com>