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I want to plot 1100(r[t]-14) vs θ[t]. How can I plot the functions of r[t] and θ[t] from NDsolve? This is my code to find r[t] and θ[t]:

m = 81;
g = 9.81;
h = 12;
l = 15;
d = 15;
a = (d - h) \[Pi]/180;

s = NDSolve[{(m*g*
   Sin[\[Theta][t]]) - (m*(r''[t] - r[t] ((\[Theta]'[t])^2))) == 
1100 (r[t] - 14), g*Cos[\[Theta][t]] == 
r[t]*\[Theta]''[t] + 2*r'[t]*\[Theta]'[t], \[Theta][0] == 
ArcSin[a/l], \[Theta]'[0] == 0, r[0] == 15, r'[0] == 0}, {r, \[Theta]}, {t, 0, 100}]

And this is code that I use to make the plot:

ParametricPlot[ Evaluate[{1100*(r[t] - 14), \[Theta][t]} /. s], {t, 0, 2}, PlotPoints -> 200]
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11
  • $\begingroup$ to use NDSolve, all parameters used need to have numerical values. $\endgroup$ Commented Apr 23, 2021 at 2:57
  • $\begingroup$ i already use ParametricPlot but i get nothing $\endgroup$ Commented Apr 23, 2021 at 3:19
  • $\begingroup$ That is not what I meant. You can't use NDSolve as you are doing. You need to provide numerical values for all the parameters in the ODE. $\endgroup$ Commented Apr 23, 2021 at 3:30
  • $\begingroup$ how can i provide numerical values $\endgroup$ Commented Apr 23, 2021 at 3:33
  • $\begingroup$ Well, it is your ODE. no one can guess what the numerical values for m and a and l. One can guess that g=9.81 assuming we are on earth. So if you want to use NDSolve, it will not work without these parameters having a numerical value. You are the only person who knows what these should be. $\endgroup$ Commented Apr 23, 2021 at 3:37

1 Answer 1

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Clear["Global`*"]

m = 81;
g = 9.81;
h = 12;
l = 15;
d = 15;
a = (d - h) π/180;

s = NDSolve[
   {(m*g*Sin[θ[t]]) - (m*(r''[t] - r[t] ((θ'[t])^2))) ==
      1100 (r[t] - 14), 
    g*Cos[θ[t]] == r[t]*θ''[t] + 2*r'[t]*θ'[t],
    θ[0] == ArcSin[a/l], θ'[0] == 0, r[0] == 15, 
    r'[0] == 0},
   {r, θ}, {t, 0, 100}];

Manipulate[
 ParametricPlot[{1100 (r[t] - 14), θ[t]} /. s[[1]], {t, 0, 
   tmax},
  AspectRatio -> 1,
  ColorFunction -> Function[{x, y, t}, ColorData["Rainbow"][t]],
  PlotLegends -> BarLegend[{"Rainbow", {0, tmax}}]],
 {{tmax, 10}, 1, 100, 1, Appearance -> "Labeled"}]

enter image description here

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2
  • $\begingroup$ oh!! i get it. It only put [1]after s right $\endgroup$ Commented Apr 23, 2021 at 3:56
  • $\begingroup$ It will plot with or without the [[1]]; however, to see the plot you cannot use the default AspectRatio $\endgroup$ Commented Apr 23, 2021 at 4:02

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