Approximated solution of Van der Pol equation describing transition from forced to free mode of oscillation

A compact expression describing the transient behaviour of the Van der Pol oscillator is presented. An original simplification on the amplitude variation leads to a new expression of the oscillation phase transient behaviour. This new expression is particularly suitable for describing oscillator relaxation, i.e. when the oscillator switches from a forced to a free oscillation state. It is shown that by choosing the injection stop instant correctly, the free running frequency can be achieved instantaneously.