Question

a swing that is 9.2m long has a child in it who is swinging. what is its period in seconds

Answer 1

The child on a swing can be modeled as a simple pendulum.  The period of a simple pendulum is given by

$T=2 \pi \sqrt{ \frac{L}{g} }=2 \pi \sqrt{ \frac{9.2m}{9.8 \frac{m}{s^2} } }=6.09s$