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

Answer: A = y/cos32

That is the amplitude A in terms of the displacement y.

Explanation: Since the displacement in the question In the question is the same in both direction, it is a Simple Harmonic Motion problem. In s. h. m the amplitude of displacement A is related to the displacement itself y by this simple equation

y = A * cos (theta)

So, A = y/cos (theta)

A = y/cos32.

If the magnitude of the displacement y is given, you just substitute in.