# How to table ParametricPlot with parametric value

I can plot this code

ClearAll["Global*"];
m = 2; a = 0;
r = 0.9;
timelimit = 35;
s = ParametricNDSolve[{m x''[t] + x'[t] ==
Cos[r t - x[t]], x[0] == a,
x'[0] == r - v}, x, {t, 0, timelimit}, {v}];
Plot[Evaluate@Table[{x[v][t] /. s, v}, {v, -8, 2, 1}], {t, 0,
timelimit}]


But If I want to parametric, using the similar structure, like this

ClearAll["Global*"];
m = 2; a = 0;
r = 0.9;
timelimit = 35;
s = ParametricNDSolve[{m x''[t] + x'[t] == Cos[r t - x[t]], x[0] == a, x'[0] == r - v}, x, {t, 0, timelimit}, {v}];
ParametricPlot[Evaluate@Table[{{r t - x[v][t], r - x[v][t]} /. s, v}, {v, -8, 2, 1}], {t, 0, timelimit}]


I can't get the output.

How can I get the Table ParametricPlot?

Thank you so much for your time!

• ParametricPlot is for 2-dimensional curves, so it needs two values. You are providing three instead: {{r t - x[v][t], r - x[v][t]} /. s, v}. Use this: {r t - x[v][t], r - x[v][t]} /. s or use ParametricPlot3D if you want 3-dimensional curves. Aug 18 at 17:21
• v is the parameter. There still are two values? r t - x[v][t] and r - x[v][t] Aug 18 at 17:34
• Yes, as I have said, use: ParametricPlot[Evaluate@Table[{r t - x[v][t], r - x[v][t]} /. s, {v, -8, 2, 1}], {t, 0, timelimit}]. Aug 18 at 17:35
• can you get the result using it? In the previous example of plot, we need to add ,v after /.s Plot[Evaluate@Table[{x[v][t] /. s, v}, {v, -8, 2, 1}], {t, 0, timelimit}] Aug 18 at 17:39
• Yes, I get a plot, you don't? It should work. But perhaps this is not the plot you actually want. Aug 18 at 17:45

As mentioned already in the comments, ParametricPlot is used for 2-dimensional curves, so you need to provide values in the form $$\{f_x, f_y\}$$:

Clear["Global*"];
m = 2; a = 0;
r = 0.9;
timelimit = 35;
s = ParametricNDSolve[{m x''[t] + x'[t] == Cos[r t - x[t]], x[0] == a,
x'[0] == r - v}, x, {t, 0, timelimit}, v];
ParametricPlot[
Evaluate@Table[{r t - x[v][t], r - x[v][t]} /. s, {v, -8, 2, 1}], {t, 0, timelimit}]


Should you want to have the parameter $$v$$ also be used as an axis, you have to use ParametricPlot3D:

ParametricPlot3D[
Evaluate@Table[{r t - x[v][t], r - x[v][t], v} /. s, {v, -8, 2, 1}], {t, 0, timelimit}]
`