A phase-fitted collocation-based Runge-Kutta-Nyström method. ... She derives collocation based Runge-Kutta-Nyström methods with symmetric points and identifies a three-stage method that is exact in phase for the linear case. The linear stability of the method is investigated by means of a symbolic-numerical package developed by M. Cafaro and the author and available at the URL: http://www.netlib.org/ode/symbolic. As a consequence of its stability properties, the method is suitable for the numerical solution of systems which exhibit a moderate stiffness. Numerical experiments are reported at the end of the paper.