Investigation of the properties of the period for the nonlinear oscillator

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 ) is well-defined for all values of the amplitude (where the initial conditions are taken to be x ( 0 ) = A and x ˙ ( 0 ) = 0 ). An approximate expression is derived for T ( A ) .