Asymptotic representations of the period for the nonlinear oscillator

The asymptotic behaviours for small and large amplitudes, A, of the period for a nonlinear oscillator, where the square of the angular frequency depends quadratically on the velocity, are obtained. These asymptotic expressions are compared with the exact period, T(A), and quite an acceptable error for a wide range of amplitudes is obtained. In addition we show that the product of the amplitude and the period, AT(A), reaches 2π when the amplitude tends to infinity.