Question

A child on a playground swings through a total of 32°. If the displacement is equal on each side of the equilibrium position, what is the amplitude of this vibration?

Answer 1

Let L = length of the swing.

Let the lowest position of the swing be the reference point.
Therefore in the lowest position,
The height of the swing = 0,
The support for the swing is at height = L.

At 32° swing relative to the vertical,
The height of the swing is
A = L - Lcos(32°) = L[1 - cos(32°)] = 0.152L

Answer:
The amplitude is 0.152*L, where L = length of the swing.