The maintenance of forced oscillations of a new type

In a paper "On a Class of Forced Oscillations" published in the Quarterly Journal of Pure and Applied Mathematics (No. 148, June, 1906), Mr. Andrew Stephenson discussed mathematically a proposition which may be stated in his own words thus: periodic non-generating force acting on a system in oscillation about a position of stable equilibrium exerts a cumulative action in intensifying or diminishing the amplitude, if its frequency is contained within any one of a number of ranges lying in the vicinity of 2μ , 2μ/2, 2μ/3 ..., where μ is the natural frequency of the system