Question about Amplitude of Oscillation

Someone asked :

A swing is 2 m long. How often do you need to push it to increase its swing's amplitude the most?

APG Institute was answering :

In the simplest case, we can consider the swing as a simple pendulum, and by calculating the rotation period of the simple pendulum, we obtain the time interval between each stroke:

T = 2π√ (L / g) = 2π√ (2/10) ≈2.8 s

If we can ignore the mass of the rope over the mass of the hanging object, then the simple pendulum assumption is acceptable. But otherwise we have to calculate the rotational inertia of the whole system and write Newton's second law for it, and by solving the resulting differential equation, we get the rotation period. (M.Sh)