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- params = {ν1 -> 1.0, ω1 -> 10.0, F -> 4.0};
- system =
- {D[x1[t], {t, 2}] == -ν1 D[x1[t], t] - ω1^2 x1[t] + F Cos[ω t], x1[0] == 1, x1'[0] == 0};
- soln = DSolve[system /. params, x1[t], t][[1]][[1]];
- Plot[x1[t] /. soln /. ω -> 8, {t, 1, 20}, Frame -> True, Axes -> False]
- amp = Table[Max[Limit[x1[t] /. soln, t -> ∞]], {ω, 1, 20, 1}]
- ListPlot[amp]
- params = {ν1 -> 40.0, ω1 -> 10.0, F -> 10.0};
- x1 = a Sin[ω t + ϕ];
- system = D[x1, {t, 2}] == -ν1 D[x1, t] - ω1^2 x1 + F Cos[ω t]
- amp = Solve[system /. params, a]
- phase = Solve[D[a /. amp, t] == 0, ϕ][[1]][[1]]
- params = {ν1 -> 1, ω1 -> 10, F -> 4};
- system = {D[ x1[t], {t, 2}] == -ν1 D[x1[t], t] - ω1^2 x1[t] + F Cos[ω t], x1[0] == 1, x1'[0] == 0};
- soln = DSolve[system /. params, x1[t], t][[1, 1]];
- (* and the steady state is*)
- lim = ((List @@ (Expand@soln[[2]])) /. x_ /; (Limit[x, t -> Infinity] == 0) :> 0)
- steadyState = Simplify@Together[Plus @@ lim]
- (* (-4 (-100 + ω^2) Cos[t ω] + 4 ω Sin[t ω])/(10000 - 199 ω^2 + ω^4) *)
- Plot[NMaxValue[steadyState, t], {ω, 1, 20}, PlotRange -> All]
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