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?
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.