Answer
The swing is pushed only once every other direction if the swing is pushed at a frequency of $\frac{f_{1}}{2}$. It is a smooth action as the swing is pushed in phase with its oscillations, and the amplitude of them motion can build up. Likewise, if it is pushed at frequency of $\frac{f_{1}}{3}$, it is pushed only once every third oscillation. And it will be pushed twice per oscillation when pushed at frequency of $2f_{1}$, but always at the extreme point in the swing.
Work Step by Step
The swing is pushed only once every other direction if the swing is pushed at a frequency of $\frac{f_{1}}{2}$. It is a smooth action as the swing is pushed in phase with its oscillations, and the amplitude of them motion can build up. Likewise, if it is pushed at frequency of $\frac{f_{1}}{3}$, it is pushed only once every third oscillation. And it will be pushed twice per oscillation when pushed at frequency of $2f_{1}$, but always at the extreme point in the swing.
