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How to Rotate a Differential Equation in a Manipulate?

I am able to rotate a completely solved parametric equation (Damped Oscillator) in a Manipulate (see attached). Problem being, I cannot figure out how to Manipulate the variables inside the equation. (Exponential damping term, Sine, Cosine, and so forth, and so on). I guess I am not defining the equation properly. Any help would be appreciated. Thanks in advance.

POSTED BY: Alan White
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Here is how you can change the exponential damping:

Clear[dosc, gR];
dosc[expDamping_] := 
  20 + (1*((Exp[-(expDamping*t)])*((4*Cos[3/10*(t - 0)]) + (4*
           Sin[3/10*(t - 0)]))));
gR[t_, r_, expDamping_] := t*Cos[r] - (dosc[expDamping])*Sin[r];
hR[t_, r_, expDamping_] := t*Sin[r] + (dosc[expDamping])*Cos[r];
Manipulate[
 ParametricPlot[{gR[t, r, expDamping], hR[t, r, expDamping]}, {t, 0, 
   75}, PlotRange -> {{-10, 100}, {-100, 50}}], {r, 
  0, -1.5}, {{expDamping, 0.02}, 0, .1}]
POSTED BY: Gianluca Gorni

Thanks very much. You have solved my problem.
POSTED BY: Alan White
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