A pure sine-wave oscillator with a fast settling time

An unforced oscillator which obeys the equation (x) double over dot + alpha(x(2) + (x) over dot (2) - 1)(x) over dot + x = 0 has a pure sine-wave limit cycle which is attained rapidly for a range of values of a. In this paper, free and forced oscillation of this equation are examined experimentally and compared with those for the Van der Pol oscillator. Asymptotic solutions for small alpha confirm the experimental results.