A child of mass is standing on a swing that may be treated as a simple pendulum of length
PHYSICS · Subjective · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics
Problem
A child of mass 25kg is standing on a swing that may be treated as a simple pendulum of length 2.5m. The child receives identical, periodic pushes from an elder brother standing behind.
(i) Define the term natural (angular) frequency of an oscillating system.
(ii) Explain, without using any mathematical expression for amplitude, why the swing attains its largest steady-state amplitude when the time interval between successive pushes is equal to the natural period of the swing.
(iii) If the brother starts pushing once every 10% shorter time than the natural period, or once every 10% longer time, predict qualitatively how the steady-state amplitude will compare with the amplitude obtained in part (ii). Justify your answer.