  The parametric instability arising when ordinary differential equations
(ODEs) are numerically integrated with Runge-Kutta-Nystr\"om (RKN) methods with
varying step sizes is investigated. It is shown that when linear constant
coefficient ODEs are integrated with RKN methods that are based on A-stable
Runge-Kutta methods, the solution is nonincreasing in some norm for all
positive step sizes, constant or varying. Perturbation methods are used to
quantify the critical step sizes associated with parametric instability.
