Investigation of the properties of the period for the nonlinear oscillator x¨+(1+x˙2)x=0

The mathematical properties of a nonlinear oscillator, having the square of the angular frequency depend quadratically on the velocity, is presented. The major conclusion is that the exact period T(A)T(A) is well-defined for all values of the amplitude (where the initial conditions are taken to be x(0)=Ax(0)=A and x˙(0)=0). An approximate expression is derived for T(A)T(A).