How to plot Vogels model in Mathametica

[mkumayl15 (amna haq)]

The formula for Vogels model is:

And it should give a graph like this:

But I’m getting just a spiral in mathametica:

My code looks like this:
Manipulate[ PolarPlot[2 Sqrt[t/2.417281], {t, 0, s}, PlotRange -> Automatic], {s, 1, 100, 1}]

Any idea how I can make the code output a spiral like how it should be in Vogels model?

[mhelmle (Michael Helmle)]

ListPlot[Table[
With[{c = 1., [Phi]0 = 137.508 Degree},
c Sqrt[n] {Cos[n [Phi]0], Sin[n [Phi]0]}], {n, 1, 80}],
PlotRange → All, AspectRatio → 1, Axes → False]

[mkumayl15 (amna haq)]

This works perfectly! Thank you!