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# NDSolve doesn't produce a smooth curve

Posted 7 months ago
 I was solving a parallel RLC circuit with NDSolve, for some reason, it doesn't give a smooth curve. Any suggestions? Thank you! eqn = c v''[t] + v'[t]/r + v[t]/l == 128000 Cos[6400 t + Pi/2] /. {r -> 50, l -> 10, c -> 1/640}; cond = {v[0] == 5, v'[0] == 11456}; sol4 = NDSolveValue[{eqn, cond}, v, {t, 0, 0.6}] Plot[sol4[t], {t, 0, 0.6}, PlotRange -> All] 
 Do DSolveValue[{eqn, cond}, v, {t, 0, 6/10}] to see what is happening. That returns Function[{t}, (5*(409272678401*Cos[(24*t)/5] + 4*(81920000*E^((32*t)/5)*Cos[6400*t] - 5597847671347*Sin[(24*t)/5] + 40959936000*E^((32*t)/5)*Sin[6400*t])))/ (409600358401*E^((32*t)/5))] Notice that includes Cos[24/5 t],Sin[24/5 t] but it also includes Cos[6400 t], Sin[6400 t] and I am guessing those last two items are a high frequency oscillation imposed on top of your much lower frequency behavior.If I use Plot[sol4[t], {t, 0, 0.06}, PlotRange -> All] the the high frequency oscillation is much more obvious. Or if I include PlotPoints->100 or PlotPoints->400 then the higher frequency is more uniformly included. I am guessing this problem is because of your very large coefficients in your equation and that you have perhaps not used sufficient steps or sufficient working precision, but that is just a guess. Or possibly there really are two very different frequencies within the differential equations that you have constructed.Study this carefully. Track down exactly the source of the problem. That should be educational.