# [✓] 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!
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Posted 1 month ago
 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.
Posted 1 month ago
 Thanks!
Posted 1 month ago
 Closely related to Kepler's Equation.
Posted 1 month ago
 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"} ]]}] ] ]