(Retreating to the relative safety of mathematics.) In the special case of "half overswing", i.e., horizontal extrema, the Fourier series comes out particularly simple (though not particularly simply): theta[t]== 2*JacobiAmplitude[(Sqrt[g/L]*t)/Sqrt[2], 2] == 4*Sum[(Sech[(1/2)*(-1 + 2*k)*Pi]* Sin[((-1 + 2*k)*Sqrt[g/L]*t*Gamma[-(1/4)]^2)/(16*Sqrt[Pi])])/(-1 + 2*k), {k, Infinity}] g Sqrt[-] t L 2 JacobiAmplitude[---------, 2] == Sqrt[2] g 1 2 (-1 + 2 k) Sqrt[-] t Gamma[-(-)] 1 L 4 Sech[- (-1 + 2 k) Pi] Sin[---------------------------------] 2 16 Sqrt[Pi] 4 Sum[------------------------------------------------------------, -1 + 2 k {k, Infinity}] Does anyone recognize this identity? The Fourier series for general swing amplitude looks a bit tougher. --rwg Incredibly, Plouffe's ISC misses 4*sech(pi/2), even with smart lookup. (The actual Fourier integral scaled this by some Gammas. Rotsa ruck.)