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[✓] Solve equation t + Sin[w t] = a in t?

Posted 1 month ago
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Hi,

Is there a way to solve (also in an approximate way) an equation of this type with Mathematica?

t + Sin[w t] = a in variable t.

Using Solve[t + Sin[w t] == a, t] can't get the solution.

Thanks!

6 Replies

General analytical solution for transcendental equation is impossible.

Approximation by numerics:

     w = 1; a = 1;

     sol = Solve[t + Sin[w t] == a, t, Reals];
     sol // N;
     (*{{t -> 0.510973}} *)

     sol2 = NSolve[t + Sin[w t] == a && -10 < t < 10, t, Reals]
     (*{{t -> 0.510973}} *)

     sol3 = FindRoot[t + Sin[w t] == a, {t, 1}]
     (*{t -> 0.510973}*)

Regards M.I.

Thanks!

Closely related to Kepler's Equation.

Interesting:)

DynamicModule[{k}, Panel[
  Column[{
    Row[{"a", " ", Slider[Dynamic[k], {1, 9, 0.3}]}], 
    With[{a = k}, 
     Dynamic@ContourPlot[t + Sin[w t] == a, {t, 0, 10}, {w, -5, 5}, 
       PlotPoints -> 25, ImageSize -> 300, 
       PlotLabel -> "w vs.t given a", FrameLabel -> {"t", "w"}
       ]]}]
  ]
 ]

sweeping

Very nice, didn't know this feature!

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