A father is about to push his child on the swing. He pulls the swing back by 1 radian, and start pushing the child with a constant force perpendicular to the swing's chain and with a magnitude equal to mg, where m is the mass of the child and the swing seat. The father stops pushing when the swing's chain is again vertical. In the approximation that sinα ≅ α (where α is an angle up to 1 radian), calculate the time the father is pushing. Neglect the weight of swing's chain and the retardation by the air drag.
Umm, some second order differential equation that I have no clue how to derive?
The Attempt at a Solution
I really have no idea where to start with this one and I only have like 4 hours to get this done . Any help would be greatly appreciated.