Thanks for looking into this. When I copy your code and run it, errors are generated:
**SetDelayed::write: Tag List in {ParametricFunction[1,InternalBag[<1>],0,1,{{\[Alpha]$370462},System
UtilitiesHashTable[<2>],{},{},{1},{Automatic,0,0}},{NDSolve
base$370469,<<1>>}][[Alpha]],ParametricFunction[1,<<4>>,{NDSolve`base$370469,<<33>>[0,<<8>>,All]}][[Alpha]],<<47>>,<<1>>,<<51>>}[[Alpha]_] is Protected. >>
Periodogram::data: Expecting a SampledSoundList, a numeric vector, or a numeric matrix instead of {<<1>>}[1.5]. >>**
I have carefully checked my typing (including the ':>' which doesn't copy/paste) -- can you see what I might be doing wrong?
emaxTime = 100; eqn = {\[CapitalTheta]''[
t] + (1/(1 - 0.1 Cos[\[Alpha] *t])) Sin[\[CapitalTheta][t] ] ==
0, \[CapitalTheta][0] == 0, \[CapitalTheta]'[0] == .1}
sol = ParametricNDSolveValue[
eqn, \[CapitalTheta], {t, 0, maxTime}, {\[Alpha] }];
alphaTable[\[Alpha]_] := Table[sol[\[Alpha]][t], {t, 0, maxTime}];
data = Flatten[
Table[Flatten[
Cases[Periodogram[alphaTable[\[Alpha]]],
Line[pts_] :> Map[Prepend[\[Alpha]], pts], All], 1], {\[Alpha],
1.5, 2.5, 0.01}], 1];
lowRange = maxTime/10;
highRange = maxTime/4;
ListPlot3D[data]