# How can I find the equation for a graph?

Posted 2 months ago
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 Hi, I use NDSolve to get this numeric solution and then plot the solution. But I also need the equation for θ(t).How can I get the θ(t) equation?thanks in advance.
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Posted 2 months ago
 Look up DSolve: Clear[g]; DSolve[{\[Theta]''[t] + g/L*Sin[\[Theta][t]] == 0, \[Theta][0] == Pi/2, \[Theta]'[0] == 0}, \[Theta][t], t] 
 You are right, it has branch cut discontinuities. But you can correct for them: solN = Block[{g = 9.8, L = 1}, NDSolveValue[{\[Theta]''[t] + g/L*Sin[\[Theta][t]] == 0, \[Theta][0] == Pi/2, \[Theta]'[0] == 0}, \[Theta], {t, 0, 10}]]; sol = DSolveValue[{\[Theta]''[t] + g/L*Sin[\[Theta][t]] == 0, \[Theta][0] == Pi/2, \[Theta]'[0] == 0}, \[Theta], t]; solDiscontinuities = FunctionDiscontinuities[ JacobiAmplitude[ 1/2 (-((Sqrt[2] Sqrt[g] t)/Sqrt[L]) + 2 EllipticF[\[Pi]/4, 2]), 2], t, Reals]; {discnt2, discnt1} = t /. Solve[solDiscontinuities, t, Reals] /. {C[1] -> 0, g -> 9.8, L -> 1}; solCorrected[t_] := sol[Mod[t, discnt2 - discnt1, discnt1]] Block[{g = 9.8, L = 1}, {Plot[solCorrected[t], {t, 0, 10}], Plot[solN[t], {t, 0, 10}]}]